Evaluate: `sin(cos^(-1)(3/5)+cos e c^(-1)(13)/5)`

Answer

`frac{63}{65}`

Explanation

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

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

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


here, `cos theta=frac{3}{5}`

`sin theta=frac{4}{5} `

Putting in above equation


`=frac{4}{5} times frac{12}{13}+frac{3}{5}+frac{5}{13} `

`=frac{4}{65}+frac{15}{65}=frac{63}{65}`