The value of $sin^{-1}\frac{3}{5}-sin^{-1}\frac{8}{17}$ is :

$cos^{-1}\frac{84}{85}$

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 $\cos A=\frac{4}{5},\cos B=\frac{15}{17}$

$⇒\cos^{-1}\left(\frac{4}{5}×\frac{15}{17}+\frac{3}{5}×\frac{8}{17}\right)$

$=\cos^{-1}\left(\frac{84}{85}\right)$