Evaluate sin [tan^−1 (2) + sin^−1 (3/5)] without using a calculator.

Answer 1

sin(A + B) = sinAcosB + cosAsinB;

tanA = 2, sinA = 2/√5; cosA = 1/√5;

sinB = 3/5, cosB= 4/5

sin[tan^-1(2) + sin^-1(3/5)] = 2/√5·4/5 + 1/√5·3/5 = 11/(5√5)