Answer :

Given: sin x + sin2x = 1


To find the value of cos12 x + 3 cos10 x + 3 cos8 x + cos6 x.


sin x = 1 – sin2x


sin x = cos2x


cos12x = sin6x, cos10x = sin5x, cos8x = sin4x, cos6x = sin3x.


Substituting above values in given equation we get


sin6x + 3sin5x + 3sin8x + sin3x [(a+b)3 = a3+3a2b+3ab2+b3]


(sin x + sin2 x)3 = (1)3


1.


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