The value of
Question:

The value of $\sin ^{-1}\left(\frac{12}{13}\right)-\sin ^{-1}\left(\frac{3}{5}\right)$ is equal to:

  1. $\pi-\sin ^{-1}\left(\frac{63}{65}\right)$

  2. $\pi-\cos ^{-1}\left(\frac{33}{65}\right)$

  3. $\frac{\pi}{2}-\sin ^{-1}\left(\frac{56}{65}\right)$

  4. $\frac{\pi}{2}-\cos ^{-1}\left(\frac{9}{65}\right)$


Correct Option: , 3

Solution:

$\sin ^{-1}\left(\frac{12}{13}\right)-\sin ^{-1}\left(\frac{3}{5}\right)$

$\sin ^{-1}\left(x \sqrt{1-y^{2}}-y \sqrt{1-x^{2}}\right)$

$=\sin ^{1}\left(\frac{33}{65}\right)=\cos ^{-1}\left(\frac{56}{65}\right)=\frac{\pi}{2}-\sin ^{1}\left(\frac{56}{65}\right)$

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