Find the exact value of the following expression without usi

Find the exact value of the following expression without using a calculator.

Solution

tan[sin^-1(-1/6) + cos^-1(-7/8)]

This is of the form tan(A+B)= (tanA+ tanB)/(1-tanA tanB)

tan(sin^-1(-1/6))

sin^-1(-1/6)=t

sin t=-1/6

tan t=1/sqrt35=sqrt35/35

tan(sin^-1(-1/6))=sqrt35/35

tan(cos^-1(-7/8))= sqrt15/7

Plug the values in the formula of tan(A+B)

(sqrt35/35) + (sqrt15/7)/(1-(sqrt 35/35)(sqrt15/7))

(7(sqrt35 +5sqrt 15))/(245 - sqrt525)