Question

Sin power 6 theta + cos power 6 theta is equal to 1 minus 3 sin square theta cos square theta

Answer 1

Answer:

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Answer 2

Answer:

sin⁶θ + cos⁶θ =1 - 3 sin²θcos²θ.

Step-by-step explanation:

Given sin⁶θ + cos⁶θ =1 - 3 sin²θcos²θ

here we have to show that sin⁶θ + cos⁶θ =1 - 3 sin²θcos²θ

that is LHS = RHS

Considering LHS  sin⁶θ+cos⁶θ

sin⁶θ+cos⁶θ = (sin²θ)³ + (cos²θ)³

it is in the form of a³ + b³ = (a+b)³ - 3 ab(a+b)

a = sin²θ, b = cos²θ

sin⁶θ+cos⁶θ = (sin²θ)³ + (cos²θ)³

= (sin²θ+cos²θ)³ - 3 sin²θcos²θ (sin²θ + cos²θ)

we know sin²θ+cos²θ =1

=(1)³- 3 sin²θcos²θ(1)

= 1 - 3 sin²θcos²θ

= RHS

Hence proved.