sin6theta+cos6theta= 1-3sin2thetacos2theta.
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Hey mate!!!
Here is the answer to your query...
sin^6A + cos^6A + 3sin^2Acos^2A
= (sin^2)^3 + (cos^2)^3 + 3sin^2Acos^2A
[a^3 + b^3 = (a+b)(a^2 + b^2 - ab)]
=(sin^2 + cos^2)(sin^4 + cos^4 - sin^2 cos^2) + 3sin^2cos^2
(sin^2 + cos^2 = 1)
=(1)(sin^4 + cos^4 - sin^2cos^2) + 3sin^2 cos^2
= sin^4 + cos^4 - sin^2cos^2 + 3sin^2 cos^2
= sin^4 + cos^4 + 2sin^2cos^2
[a^2 + b^2 + 2ab = (a+b)^2]
= (sin^2 + cos^2)^2
=(1)^2
= 1 RHS
sin^6A + cos^6A + 3sin^2Acos^2A
= (sin^2)^3 + (cos^2)^3 + 3sin^2Acos^2A
[a^3 + b^3 = (a+b)(a^2 + b^2 - ab)]
=(sin^2 + cos^2)(sin^4 + cos^4 - sin^2 cos^2) + 3sin^2cos^2
(sin^2 + cos^2 = 1)
=(1)(sin^4 + cos^4 - sin^2cos^2) + 3sin^2 cos^2
= sin^4 + cos^4 - sin^2cos^2 + 3sin^2 cos^2
= sin^4 + cos^4 + 2sin^2cos^2
[a^2 + b^2 + 2ab = (a+b)^2]
= (sin^2 + cos^2)^2
=(1)^2
= 1 RHS