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sin^6 x+cos^6x +3sin^2x cos^2x =1

sin^6 x+cos^6x +3sin^2x cos^2x =1

Grade:6

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
Dear student,
If your ques is that To prove the identity sin^6x+cos^6x+3sin^2xcos^2x=1
then your solution is :
L.H.S.= sin^6x+cos^6x+3 sin^2xcos^2x
using formula a^3+b^3=(a+b)(a^2+b^2-ab), we get
(sin^2x+cos^2x){ sin^4x+cos^4x-sin^2xcos^2x} + 3 sin^2xcos^2x
=sin^4xcos^4x+2sin^2xcos^2x
=(sin^2x+cos^2x)^2
=1

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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