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prove the identity

(sinX)^6 +(cosX)^6= 1 - 3(sinX)^2 (cosX)^2

sinX^6= sinx^2 ^3 = (1-cosX^2)^3
= (1-2CosX^2 + cos^4) (1-cosX^2)
then multiply that out
1-2CosX^2 + cos^4 - cosX^2 + 2cos^4 -cos^6

add that on the left to the cos^6, and combine terms..
1-3CosX^2 + 3cos^4
1-3cos^2x (i-cos^2 x)

then use the sin^2 x=1-cos^2 x and you have it.

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