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Prove that:tan^(-1)(63/16)=sin^(-1)(5/13...

Prove that:`tan^(-1)(63/16)=sin^(-1)(5/13)+cos^(-1)(3/5)`

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To prove that \( \tan^{-1}\left(\frac{63}{16}\right) = \sin^{-1}\left(\frac{5}{13}\right) + \cos^{-1}\left(\frac{3}{5}\right) \), we will start with the right-hand side and simplify it step by step. ### Step 1: Define the angles Let: \[ \theta = \sin^{-1}\left(\frac{5}{13}\right) \] \[ ...
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