Prove the following results: `tan(sin^(-1)(15)/(13)+cos^(-1)3/5)=(63)/(16)` (ii) `sin(cos^(-1)3/5+sin^(-1)5/(13))=(63)/(65)`

Answer

=`frac{63}{65}`

Explanation

`\sin (\frac{\cos ^{-1} 3}{5}+{ cosec }-1 \frac{13}{5})`


`=\sin (\frac{\cos ^{-1} 3}{5}) \cos ({ cosec } \frac{}{-1} \frac{13}{5})+\cos (\frac{\cos ^{-1} 3}{5})`


`\sin (\cosec ^{-1} \frac{13}{5})`


`=\sin (\frac{\sin ^{-1} 4}{5}) \cos (\frac{\cos ^{-1} 12}{13})+\cos (\frac{\cos ^{-1} 3}{5}) \sin (\frac{\sin ^{-1} 5}{13})`


`\frac{4}{5} \times \frac{12}{13} \times \frac{3}{5} \times \frac{5}{13}=\frac{63}{65}`