Prove that:
               \sin^{-1}\frac{4}{5}+\tan^{-1}\frac{5}{12}+\cos^{-1}\frac{63}{65}= \frac{\pi }{2}

 

 

 

 
 
 
 
 

Answers (1)

LHS: \sin^{-1}\frac{4}{5}+\tan^{-1}\frac{5}{12}+\cos^{-1}\frac{63}{65}
\Rightarrow = \tan^{-1}\frac{4}{3}+\tan^{-1}\frac{5}{12}+\cos^{-1}\frac{63}{65}
\Rightarrow = \tan^{-1}\frac{\frac{4}{3}+\frac{5}{12}}{1-\frac{4}{3}\times \frac{5}{12}}+\cos^{-1}\frac{63}{65}
\Rightarrow = \tan^{-1}\frac{63}{16}+\cot ^{-1}\frac{63}{16}
\Rightarrow \frac{\pi }{2}= RHS

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