Question

Prove that sin^6 a + cos^6 a = 3sin^4 a + 3cos^2 a - 2​

Answer 1

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(sin
2
θ+cos
2
θ)
3
+3sin
2
θcos
2
θ

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