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if sin x +sin^2 x + sin^3 x = 1 then cos^6 x - 4 cos^4 x +9cos^2 x = ?

if sin x +sin^2 x + sin^3 x = 1
then cos^6 x - 4 cos^4 x +9cos^2 x = ?

Grade:

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
sinx+sin^3x=1-sin^2x
sinx+sin^3x=cos^2x
sinx(1+sin^2x)=cos^2x
sinx(1+1-cos^2x)=cos^2x
sinx(2-cos^2x)=cos^2x
squaring both sides
sin^2x(2-cos^2x)^2=cos^4x
sin^2x(4+cos^4x-4cos^2x)=cos^4x
(1-cos^2x)(4+cos^4x-4cos^2x)=cos^4x
4+cos^4x-4cos^2x-4cos^2x-cos^6x+4cos^4x=cos^4x
4-cos^6x-8cos^2x+4cos^4x=0
cos^6x-4cos^4x+8cos^2x=4
Thanks & Regards
Rinkoo Gupta
askIITians Faculty

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