Prove the following

Question:

If $\alpha=\cos ^{-1}\left(\frac{3}{5}\right), \beta=\tan ^{-1}\left(\frac{1}{3}\right)$, where $0<\alpha, \beta<\frac{\pi}{2}$, then $\alpha-\beta$ is equal to :

 

  1. $\sin ^{-1}\left(\frac{9}{5 \sqrt{10}}\right)$

  2. $\tan ^{-1}\left(\frac{9}{14}\right)$

  3. $\cos ^{-1}\left(\frac{9}{5 \sqrt{10}}\right)$

  4. $\tan ^{-1}\left(\frac{9}{5 \sqrt{10}}\right)$


Correct Option: 1

Solution:

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