Question

Prove
sin^6theta- cos^6 theta= (2cos^2theta-1) (1-sin^2theta.cos^2theta)

Answer 1

Answer:

sin 6θ+cos 6 θ+3sin2θcos2θ⇒LHS=(sin 2 θ)

3+(cos 2 θ) 3 +3sin 2 θcos 2 θ

Using, [a 3 +b 3 =(a+b) 3 −3ab(a+b)]⇒LHS=(sin 2 θ+cos 2 θ)

3 −3sin 2 θcos 2 θ(sin 2 θ+cos 2 θ)

3 +3sin 2 θcos 2 θ⇒LHS=1−3sin 2 θcos 2 θ+3sin2 θcos 2 θ=1=RHS