1.

If cos x + cos^2 x = 1, then the value of sin^4x + sine^6x is equal to

Answer»

Since cosx+cos^2x=1, then cosx=1-cos^2x=sin^2x.Thensin^12x+3sin^10x+3 sin^8x+sin^6x+2 sin^4x+2sin^2x-2= cos^6x+3cos^5x+3 cos^4x+cos^3x+2 cos^2x+2cosx-2=cos^6x+3cos^5x+3 cos^4x+cos^3x=cos^4x (cos^2x+3) + cos^3x(3cos^2+1)= cos^4x (1-cosx+3) +cos^3x(3-3cosx+1)= (1-cosx)^2 (4-cosx)+cosx((1-cosx)(4-3cosx)= (1-2cosx+1-cosx)(4-cosx)+cosx(4-7cosx+3-...= (2-3cosx)(4-cosx)+ cosx(7-10cosx)= 8-14cosx+3cos^2x+7cosx-10cos^2x= 8-7cosx-7cos^2x=8-7(1)= 1


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