Question

Prove that 6(sin⁶ θ+cos⁶ θ)-9(sin⁴ θ+cos⁴ θ)=-3




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Answer 1

Answer:

2(sin6θ + cos6θ) – 3 (sin4θ + cos4θ) + 1

= 2[(sin2θ)3 + (cos2θ)3] – 3[(sin2θ)2 + (cos2θ)2] + 1

=2[(sin2θ + cos2θ)3 – 3 sin2θ cos2θ (sin2θ + cos2θ)] -3[(sin2θ + cos2θ)2

– 2 sin2θ cos2θ] + 1

Using the identity sin2A + cos2A = 1,

= 2[1 – 3 sin2θ cos2θ] – 3[-2 sin2θ cos2θ] + 1

= 2 – 6 sin2θ cos2θ -3 + 6 sin2θ cos2θ + 1

Step-by-step explanation:

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