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If `sinx+ sin^2x =1`, then` cos^8x+ 2cos^6x +cos^4x `=(A) 2 (B) 1 (C) 3 (D) `1/2`

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If `sinx+ sin^2x =1`, then` cos^8x+ 2cos^6x +cos^4x `=(A) 2 (B) 1 (C) 3 (D) `1/2`
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`sinx+sin^2=1`
`sinx=1-sin^2x`
`sinx=cos^2x-(1)`
`cos^8x+2cos^6x+cos^4x`
from equation 1
`sin^4x+2sin^3x+sin^2x`
`sin^2x(sin^2x+2sinx+1)`
`sin^2x(sinx+1)^2`
`(sinx(sinx+1))^2`
`(sin^2x+sinx)^2`
`1^2=1`.
Equation B is correct.
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