Question 1

Find the exact value. $\cos 95 ^ { \circ } \cos 50 ^ { \circ } + \sin 95 ^ { \circ } \sin 50 ^ { \circ }$

Accepted Answer

A)    32/23 \sqrt { 2 } / 232c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​/2 
B)    2/2\sqrt { 2 } / 22c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​/2 
C)    111 
D)    −3/2- \sqrt { 3 } / 2−3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​/2 
E)   none  B

Question 2

Find the exact value. $\sin 75 ^ { \circ }$

Accepted Answer

A)    6+2\sqrt { 6 } + \sqrt { 2 }6c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​+2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​ 
B)    6−2\sqrt { 6 } - \sqrt { 2 }6c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​−2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​ 
C)    6+24\frac { \sqrt { 6 } + \sqrt { 2 } } { 4 }46c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​+2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​​ 
D)    6+324\frac { \sqrt { 6 } + 3 \sqrt { 2 } } { 4 }46c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​+32c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​​ 
E)    6+22\frac { \sqrt { 6 } + \sqrt { 2 } } { 2 }26c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​+2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​​ C

Question 3

Find the exact value. $\cos 85 ^ { \circ } \cos 40 ^ { \circ } + \sin 85 ^ { \circ } \sin 40 ^ { \circ }$

Accepted Answer

A)    322\frac { 3 \sqrt { 2 } } { 2 }232c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​​ 
B)    22\frac { \sqrt { 2 } } { 2 }22c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​​ 
C)    111 
D)    −32- \frac { \sqrt { 3 } } { 2 }−23c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​​ 
E)   none  B

Question 4

Find the exact value. $\cos \left( 2 \tan ^ { - 1 } \frac { 7 } { 24 } \right)$

Accepted Answer

The answer of Find the exact value. \(\cos \left( 2...

Question 5

Find $\sin 2 x$ , given that $\sin x = 3 / 5$ and $x$ is in quadrant II.

Accepted Answer

The answer of Find $\sin 2 x$ , given that...

Question 6

Write the sum as a product. $\sin 4 x + \sin 5 x$

Accepted Answer

The answer of Write the sum as a product. \(\sin...

Question 7

Find the exact value. $\cos ^ { 2 } ( \pi / 8 ) - \sin ^ { 2 } ( \pi / 8 )$

Accepted Answer

The answer of Find the exact value. \(\cos ^ {...

Question 8

Find the exact value of $\sin ( x + y )$ given that $\sec x = 3 / 2 , \csc y = 3$ , and x and y are in quadrant I.

Accepted Answer

The answer of Find the exact value of \(\sin (...

Question 9

Find the exact value. $\frac { \tan 10 ^ { \circ } + \tan 20 ^ { \circ } } { 1 - \tan 10 ^ { \circ } \tan 20 ^ { \circ } }$

Accepted Answer

The answer of Find the exact value. \(\frac { \tan...

Question 10

Use a double-angle formula or half-angle formula to simplify $\frac { \sin 48 ^ { \circ } } { 1 + \cos 48 ^ { \circ } }$

Accepted Answer

A)    tan⁡48∘	an 48 ^ { \circ }tan48∘ 
B)    tan⁡24∘	an 24 ^ { \circ }tan24∘ 
C)    csc⁡24∘\csc 24 ^ { \circ }csc24∘ 
D)    cot⁡48∘\cot 48 ^ { \circ }cot48∘ 
E)    1+sin⁡24∘1 + \sin 24 ^ { \circ }1+sin24∘

Question 11

Solve the equation in the interval $[ 0,2 \pi )$ . $2 \cos ^ { 2 } x + \sin x = 1$

Accepted Answer

A)    π6,π2\frac { \pi } { 6 } , \frac { \pi } { 2 }6π​,2π​ 
B)    π6,π3\frac { \pi } { 6 } , \frac { \pi } { 3 }6π​,3π​ 
C)    π2,7π6\frac { \pi } { 2 } , \frac { 7 \pi } { 6 }2π​,67π​ 
D)    π6,11π6\frac { \pi } { 6 } , \frac { 11 \pi } { 6 }6π​,611π​ 
E)   none

Question 12

Use a graphing device to find the solution of $\sin 4 x = x$ , correct to two decimal places

Accepted Answer

A)    000 ,  ±0.62\pm 0.62±0.62 
B)    ±0.25\pm 0.25±0.25 
C)    −1- 1−1 ,  ±0.62\pm 0.62±0.62 
D)    ±1\pm 1±1 
E)    0,±0.120 , \pm 0.120,±0.12

Question 13

Solve the equation in the interval $[ 0,2 \pi )$ 
. $\cos ^ { 2 } x = \cos x + 6$

Accepted Answer

The answer of Solve the equation in the interval \([...

Question 14

Verify the identity. $\frac { 1 + \sec ^ { 2 } x } { 1 + \tan ^ { 2 } x } = 1 + \cos ^ { 2 } x$

Accepted Answer

The answer of Verify the identity. \(\frac { 1 +...

Question 15

Find the exact value. $\sin \left( 2 \tan ^ { - 1 } \frac { 5 } { 12 } \right)$

Accepted Answer

A)    5/65 / 65/6 
B)    12/512 / 512/5 
C)    119/120119 / 120119/120 
D)    120/169120 / 169120/169 
E)   none of these

Question 16

$\cos ( x + y ) = \cos x + \cos y$

Accepted Answer

A) True 
 B)False

Question 17

Find the exact value of the expression. $\cos \left( \sin ^ { - 1 } ( \sqrt { 3 } / 2 ) + \tan ^ { - 1 } ( \sqrt { 3 } ) \right]$

Accepted Answer

The answer of Find the exact value of the expression....

Question 18

Write the product as a sum. $\cos 7 x \cos 3 x$

Accepted Answer

The answer of Write the product as a sum. \(\cos...

Question 19

Prove the identity. $\cos \left( x + \frac { \pi } { 2 } \right) + \sin \left( x + \frac { \pi } { 2 } \right) = \cos x - \sin x$

Accepted Answer

The answer of Prove the identity. \(\cos \left( x +...

Question 20

Find the exact value. $\frac { \tan 35 ^ { \circ } + \tan 10 ^ { \circ } } { 1 - \tan 35 ^ { \circ } \tan 10 ^ { \circ } }$

Accepted Answer

A)    −1- 1−1 
B)    22\frac { \sqrt { 2 } } { 2 }22c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z"/>​​ 
C)    111 
D)    π4\frac { \pi } { 4 }4π​ 
E)   none

Exam 8: Polar Coordinates and Parametric Equations

Find the exact value. cos⁡95∘cos⁡50∘+sin⁡95∘sin⁡50∘\cos 95 ^ { \circ } \cos 50 ^ { \circ } + \sin 95 ^ { \circ } \sin 50 ^ { \circ }cos95∘cos50∘+sin95∘sin50∘

Find the exact value. sin⁡75∘\sin 75 ^ { \circ }sin75∘

Find the exact value. cos⁡85∘cos⁡40∘+sin⁡85∘sin⁡40∘\cos 85 ^ { \circ } \cos 40 ^ { \circ } + \sin 85 ^ { \circ } \sin 40 ^ { \circ }cos85∘cos40∘+sin85∘sin40∘

Find the exact value. cos⁡(2tan⁡−1724)\cos \left( 2 \tan ^ { - 1 } \frac { 7 } { 24 } \right)cos(2tan−1247​)

Find sin⁡2x\sin 2 xsin2x , given that sin⁡x=3/5\sin x = 3 / 5sinx=3/5 and xxx is in quadrant II.

Write the sum as a product. sin⁡4x+sin⁡5x\sin 4 x + \sin 5 xsin4x+sin5x

Find the exact value. cos⁡2(π/8)−sin⁡2(π/8)\cos ^ { 2 } ( \pi / 8 ) - \sin ^ { 2 } ( \pi / 8 )cos2(π/8)−sin2(π/8)

Find the exact value of sin⁡(x+y)\sin ( x + y )sin(x+y) given that sec⁡x=3/2,csc⁡y=3\sec x = 3 / 2 , \csc y = 3secx=3/2,cscy=3 , and x and y are in quadrant I.

Find the exact value. tan⁡10∘+tan⁡20∘1−tan⁡10∘tan⁡20∘\frac { \tan 10 ^ { \circ } + \tan 20 ^ { \circ } } { 1 - \tan 10 ^ { \circ } \tan 20 ^ { \circ } }1−tan10∘tan20∘tan10∘+tan20∘​

Use a double-angle formula or half-angle formula to simplify sin⁡48∘1+cos⁡48∘\frac { \sin 48 ^ { \circ } } { 1 + \cos 48 ^ { \circ } }1+cos48∘sin48∘​

Solve the equation in the interval [0,2π) [ 0,2 \pi ) [0,2π) . 2cos⁡2x+sin⁡x=12 \cos ^ { 2 } x + \sin x = 12cos2x+sinx=1

Use a graphing device to find the solution of sin⁡4x=x\sin 4 x = xsin4x=x , correct to two decimal places

Solve the equation in the interval [0,2π)[ 0,2 \pi )[0,2π) . cos⁡2x=cos⁡x+6\cos ^ { 2 } x = \cos x + 6cos2x=cosx+6

Verify the identity. 1+sec⁡2x1+tan⁡2x=1+cos⁡2x\frac { 1 + \sec ^ { 2 } x } { 1 + \tan ^ { 2 } x } = 1 + \cos ^ { 2 } x1+tan2x1+sec2x​=1+cos2x

Find the exact value. sin⁡(2tan⁡−1512) \sin \left( 2 \tan ^ { - 1 } \frac { 5 } { 12 } \right) sin(2tan−1125​)

cos⁡(x+y)=cos⁡x+cos⁡y\cos ( x + y ) = \cos x + \cos ycos(x+y)=cosx+cosy

Find the exact value of the expression. cos⁡(sin⁡−1(3/2)+tan⁡−1(3)]\cos \left( \sin ^ { - 1 } ( \sqrt { 3 } / 2 ) + \tan ^ { - 1 } ( \sqrt { 3 } ) \right]cos(sin−1(3​/2)+tan−1(3​)]

Write the product as a sum. cos⁡7xcos⁡3x\cos 7 x \cos 3 xcos7xcos3x

Prove the identity. cos⁡(x+π2)+sin⁡(x+π2)=cos⁡x−sin⁡x\cos \left( x + \frac { \pi } { 2 } \right) + \sin \left( x + \frac { \pi } { 2 } \right) = \cos x - \sin xcos(x+2π​)+sin(x+2π​)=cosx−sinx

Find the exact value. tan⁡35∘+tan⁡10∘1−tan⁡35∘tan⁡10∘\frac { \tan 35 ^ { \circ } + \tan 10 ^ { \circ } } { 1 - \tan 35 ^ { \circ } \tan 10 ^ { \circ } }1−tan35∘tan10∘tan35∘+tan10∘​