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If sintheta+sin^(2)theta=1, then prove t...

If `sintheta+sin^(2)theta=1`, then prove that `cos^(12)theta+3cos^(10)theta+3cos^(8)theta+cos^(6)theta-1=0`

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Given that `sintheta=1-sin^(2)theta=cos^(2)theta`
LHS `=cos^(6)theta(cos^(2)theta+1)^(3)-1=sin^(3)theta(1+sintheta)^(3) -1=(sintheta+sin^(2)theta)^(3)-1=1-1=0`
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