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Prove that:cos^(-1)(12/13)+sin^(-1)(3/5)...

Prove that:`cos^(-1)(12/13)+sin^(-1)(3/5)=sin^(-1)(56/65)`

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To prove that \( \cos^{-1}\left(\frac{12}{13}\right) + \sin^{-1}\left(\frac{3}{5}\right) = \sin^{-1}\left(\frac{56}{65}\right) \), we will follow these steps: ### Step 1: Express \( \cos^{-1}\left(\frac{12}{13}\right) \) in terms of sine We know that: \[ \cos^{-1}(x) = \frac{\pi}{2} - \sin^{-1}(x) \] Thus, we can write: ...
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