Math, asked by natashaa67, 1 year ago

sin^6+cos^6+3sin²cos²

Answers

Answered by bhaveshjain281
3

Using simple formula a³+b³=(a+b)(a²-ab+b²) and a²+b²=(a+b)²-2ab
And identity sin²x+cos²x=1

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bhaveshjain281: Ans is 1 mark brainliest if you have understood .
Answered by mathsdude85
1

Solution :

Now, LHS = sin⁶θ + cos⁶θ

= (sin²θ)³ + (cos²θ)³

= (sin²θ + cos²θ) {(sin²θ)² + (cos²θ)² - sin²θ cos²θ}

= 1 * {(sin²θ + cos²θ)² - 2sin²θ cos²θ - sin²θ cos²θ}

= 1 - 3 sin²θ cos²θ

= RHS (Proved)

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