Question

Prove the following result

`sin(cos^-1  3/5+sin^-1  5/13)=63/65`

Answer 1

LHS  `=sin(cos^-1  3/5+sin^-1  5/13)`

`=sin[sin^-1sqrt(1-(3/5)^2)+sin^-1  5/13]`

`=sin[sin^-1  4/5+sin^-1  5/13]`

`=sin{sin^-1[4/5xxsqrt(1-(5/13)^2)+5/13xxsqrt(1-(4/5)^2)]}`

`=sin[sin^-1(48/65+15/65)]`

`=sin(sin^-1  63/65)`

`=63/65 =`RHS