SOLUTION: PROVE THAT COS^6A+SIN^6A=1-3SIN^2ACOS^2A

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Question 325583: PROVE THAT COS^6A+SIN^6A=1-3SIN^2ACOS^2A
Answer by AAfter Search(61) About Me  (Show Source):
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To prove COS^6A+SIN^6A=1-3SIN^2ACOS^2A
L.H.S. = COS^6A+SIN^6A
= (cos^2A)^3 + (sin^2A)^3
= (cos^2A + sin^2A)^3 -3cos^2Asin^2A(cos^2A + sin^2A)^2
= 1^3 -3cos^2Asin^2A(1)^2 [since, sin^2A + cos^2A = 1]
= 1 - 3cos^2Asin^2A = R.H.S.
Hence, Proved