Question

Prove that sin^6 theta + cos^6 theta is equal to 1- 3 sin^2 theta * cos^2 theta

Answer 1

sin^6 theta + cos^6 theta

(sin^2 theta)^3 + (cos^2 theta)^3

(sin^2 theta+cos^2 theta)^3-3*cos^2 theta*sin^2 theta*(sin^2 theta+cos^2 theta)

1-3cos^2 theta*sin^2 theta