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Prove that cos^(-1)4/5cos^(-1)(12)/(13)=...

Prove that `cos^(-1)4/5cos^(-1)(12)/(13)=cos^(-1)(33)/(65)`

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To prove that \( \cos^{-1}\left(\frac{4}{5}\right) + \cos^{-1}\left(\frac{12}{13}\right) = \cos^{-1}\left(\frac{33}{65}\right) \), we will use the identity for the sum of inverse cosines: \[ \cos^{-1}(x) + \cos^{-1}(y) = \cos^{-1}(xy - \sqrt{(1-x^2)(1-y^2)}) \] ### Step 1: Identify \( x \) and \( y \) Let: ...
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