Write the Trigonometric Expression as an Algebraic Expression Containing U $\sin \left( \tan ^ { - 1 } \mathrm { u } - \tan ^ { - 1 } \mathrm { v } \right)$

Multiple Choice

Write the trigonometric expression as an algebraic expression containing u and v.
- $\sin \left( \tan ^ { - 1 } \mathrm { u } - \tan ^ { - 1 } \mathrm { v } \right)$

A) $\frac { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } } { 1 - u v }$
B) $\frac { 1 - u v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$
C) $\frac { u - v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$
D) $\frac { 1 + u v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$