1.

The value of `sin^(8)theta+cos^(8)theta+sin^(6)theta cos^(2)theta+3sin^(4)theta cos^(2)theta+cos^(6)theta sin^(2)theta+3sin^(2)thetacos^(4)theta` is equal toA. `cos^(2)2 theta`B. `sin^(2)2theta`C. `cos^(3)2 theta+sin^(3)2theta`D. none of these

Answer» Correct Answer - D
We have,
`sin^(8)theta+cos^(8)theta+sin^(6)thetacos^(2)theta+3 sin^(4)thetacos^(2)theta cos^(6)thetasin^(2)theta+3sin^(2)thetacos^(4)theta`
`=sin^(8)theta+cos^(8)theta+sin^(2)thetacos^(2)theta(sin^(4)theta+cos^(4)theta+3sin^(2)theta+3cos^(2)theta)`
`=(sin^(4)theta+cos^(4)theta)^(2)-2sin^(4)thetacos^(4)theta`
`+1/4sin^(2)2 theta{(sin^(2)theta+cos^(2)theta)^(2)-1/2sin^(2)2 theta+3}`
`=(1-(sin^(2)2theta)/(4))^(2)=1/8sin^(4)2theta+sin^(2)2theta-1/8sin^(4)2theta`
`=1+1/2sin^(2)2theta-3/16sin^(4)2theta`
`=1/16(16+8sin^(2)2theta-3sin^(4)2theta)`


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