Question

Prove that cos6 θ + sin6 θ = 1 – 3cos2 θ sin2 θ. Pls give answer quickly.

Answer 1

L.H.S. =sin

6

θ+cos

6

θ

=(sin

2

θ)

3

+(cos

2

θ)

3

Put sin

2

θ=a and cos

2

θ=b

∴ L.H.S. =a

3

+b

3

=(a+b)

3

−2ab(a+b)

=(sin

2

θ−cos

2

θ)

3

−3sin

2

θcos

2

θ(sin

2

θ+cos

2

θ)

=(1)

3

−3sin

2

θcos

2

θ[∵sin

2

θ+cos

2

θ=1]

=1−3sin

2

θcos

2

θ

= R.H.s

answer in photo

thanks