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) $\frac { 1 + u v } { \sqrt { u ^ { 2 } + 1 } \cdot \sqrt { v ^ { 2 } + 1 } }$

Question

Quizplus · Accepted Answer

The expression $\sin(\tan^{-1}u - \tan^{-1}v)$ can be simplified using the difference formula for sine and the identity for $\tan^{-1}$, leading to the algebraic expression $\frac{u-v}{\sqrt{u^2+1}\cdot\sqrt{v^2+1}}$.

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

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