Question

prove that sin6teta + cos6teta + cos2teta +sin2teta =1

Answer 1

Answer:

Hence proved

Step-by-step explanation:

sin 6 θ+cos 6 θ+3sin 2 θcos 2 θ

⇒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(sin2θ+cos 2 θ) 3 +3sin 2 θcos 2 θ

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