Question

Prove that sin^6a+cos^6a=3 sin^4 a+3 cos^2a-2​

Answer 1

Answer:

We can prove the above by:

2(sin6a+cos6a) - 3(sin4a+cos4a)+1=0 (on solving )

=2[(sin2a)3+(cos2a)3] - 3[(sin2a)2+(cos2a)2] + 1 =2[(sin2a+cos2a)3 -3sin2a cos2a (sin2a+cos2a)] -3[(sin2a+cos2a)2 -2sin2acos2a] + 1 =2[1-3sin2acos2a] -3[1-2sin2a cos2a] + 1 =2 - 6sin2a cos2a - 3 + 6sin2a cos2a + 1 =0

proved.__