Prove that `sin^(-1)(8/(17))+sin^(-1)(3/5)=cos^(-1)((36)/(85))`

Explanation

Here, we will use,

`sin^-1x+sin^-1y = sin^-1(xsqrt(1-y^2)+ysqrt(1-x^2))`

`L.H.S. = sin^-1(8/17)+sin^-1(3/5)`

`=sin^-1(8/17sqrt(1-(3/5)^2)+3/5sqrt(1-(8/17)^2))`

`=sin^-1(8/17(4/5)+3/5(15/17))`

`=sin^-1(32/85+45/85)`

`=sin^-1(77/85)`

`=cos^-1(sqrt(1-(77/85)^2))`

...