Question

Evaluate: sin6 theta - cos6 theta

Answer 1

Heya!

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Sin 6x - Cos 6x = √2 Cos ( 6x + 45 )

Where x = theta

Answer 2

Answer:

sin⁶Θ - cos⁶Θ

= (sin²Θ)³ - (cos²Θ)³

= (sin²Θ - cos²Θ)(sin⁴Θ + cos⁴Θ + sin²Θ.cos²Θ)   ...(1)

sin⁴Θ + cos⁴Θ = (sin²Θ + cos²Θ)² - 2sin²Θcos²Θ   ...(2)

Substituting (2) in (1), we get ⇒

sin⁶Θ - cos⁶Θ = (sin²Θ - cos²Θ)(1 - sin²Θ²cosΘ)

We can simplify further, but it will lead to a really lengthy answer.

That's why, i stopped at this step.

Hope you understood the answer...