Question

Prove the following result

`cos(sin^-1  3/5+cot^-1  3/2)=6/(5sqrt13)`

Answer 1

LHS = `cos(sin^-1  3/5+cot^-1  3/2)`

`=cos(sin^-1  3/5+tan^-1  2/3)`

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

`=cos(cos^-1  4/5+cos^-1  3/sqrt13)`

`=cos{cos^-1[4/5xx3/sqrt13-sqrt(1-(4/5)^2)sqrt(1-(3/sqrt13)^2]}`

`=cos{cos^-1[12/(5sqrt13)-6/(5sqrt13)]}`

`=cos{cos^-1[6/(5sqrt13)]}`

`=6/(5sqrt13)=`RHS