Math, asked by cricketergaganpradha, 7 hours ago

sin³ a - cos³ a = (sin²a - cos²a)(1 - 2 sin²a .cos²a)​

Answers

Answered by Sanskar260
1

The question is a bit wrong.

It should be sin⁸a - cos⁸ a = (sin²a - cos²a)(1 - 2 sin²a .cos²a)

sin⁸a - cos⁸a

= (sin⁴a)² - (cos⁴a)²

= (sin⁴a + cos⁴a)(sin⁴a - cos⁴a)

= ((sin²a)² + (cos²a)² + 2sin²a.cos²a - 2sin²a.cos²a) (sin²a + cos²a)(sin²a - cos²a)

= ((sin²a + cos²a)²- 2sin²a.cos²a) ( 1 ) (sin²a - cos²a)

= ((1)²- 2sin²a.cos²a) (sin²a - cos²a)

= (sin²a - cos²a)(1 - 2sin²a.cos²a)

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