The value of $sin^{-1}\frac{3}{5}-sin^{-1}\frac{8}{17}$ is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\cos^{-1}\frac{84}{85}$
$\sin^{-1}\frac{3}{5}-\sin^{-1}\frac{8}{17}$
so $\cos^{-1}\cos\left(\sin^{-1}\frac{3}{5}-\sin^{-1}\frac{8}{17}\right)≡\cos(A-B)$
$=\cos A\cos B+\sin A\sin B$
$\sin A=\frac{3}{5},\sin B=\frac{8}{17}$
so $\cos A=\frac{4}{5},\cos B=\frac{15}{17}$
$⇒\cos^{-1}\left(\frac{4}{5}×\frac{15}{17}+\frac{3}{5}×\frac{8}{17}\right)$
$=\cos^{-1}\left(\frac{84}{85}\right)$