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If sintheta+sin^2theta=1, then prove tha...

If `sintheta+sin^2theta=1,` then prove that `cos^(12)theta+3cos^10theta+3cos^8theta+cos^6theta+2cos^4theta+2cos^2theta-2=1`

Text Solution

Verified by Experts

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