Question

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

Answer 1

`cos(sin^-1  3/5+sin^-1  5/13)=cos{sin^-1(3/5sqrt(1-(5/13)^2)+5/13sqrt(1-(3/5)^2))}`

`=cos{sin^-1(3/5xx12/13+5/13xx4/5)}`

`=cos{sin^-1(36/65+4/13)}`

`=cos{sin^-1(56/65)}`

`=cos{cos^-1sqrt(1-(56/65)^2)}`          `[because sin^-1x=cos^-1sqrt(1-x^2)]`

`=cos{cos^-1  33/65}`

`=33/65`