Question

sin⁶a + cos⁶a = 1-3 sin²a cos²a​

Answer 1

$\bold{AnsweR:}$

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Step-by-step explanation:

sin^6A + cos^6A ,

= (sin^2A)3 + (cos^2A)3 ,

= (sin^2A + cos^2A)(sin^4A – sin^2Acos^2A + cos^4A) ,

= 1 (sin^4A – sin^2Acos^2A + cos^4A + 2sin^2Acos^2A – 2sin^2Acos^2A) ,

= (sin2A + cos2A) – 3sin2Acos2A ,

= 1 – 3sin^2Acos^2A.

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Answer 2

Answer:

sin^6A + cos^6A

= (sin^2A)3 + (cos^2A)3

= (sin^2A + cos^2A)(sin^4A – sin^2Acos^2A + cos^4A)

= 1 (sin^4A – sin^2Acos^2A + cos^4A + 2sin^2Acos^2A – 2sin^2Acos^2A)

= (sin2A + cos2A) – 3sin2Acos2A

= 1 – 3sin^2Acos^2A

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