Question

if sinx+sin^2x=1 then cos^12x+cos^10x+cos^8x+cos^6x=??

Answer 1

Answers................

sinx+sinx2 =1

sinx+sinx2 =sinx2 +cosx2 

sinx+sinx2 =sinx2 +cosx2

sinx=cosx2

sinx2 +cosx2 =1

(sinx2 +cosx2 )3=13 

sinx6 +cosx6 +3cos2 sin2 (sinx2 +cosx2 )=1

sinx6 +cosx6 =1-3cos2 sin2  

cos12x+3cos10x+3cos8x+cos6x

Thus

sin6 +cos6 +3sin5x+3sin4x

1-3cos2 sin2  +3sin3x(sin2x +sinx)

sinx=cos2x

1-3sin3  +3sin3x(sin2x +sinx)

sinx+sin2x=1

1-3sin3  +3sin3x

Ans =1

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