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4(sin^(6)theta+cos^(6)theta)-6(sin^(4)th...

`4(sin^(6)theta+cos^(6)theta)-6(sin^(4)theta+cos^(4)theta)`is equal to

A

0

B

1

C

`-2`

D

none of these

Text Solution

Verified by Experts

`4[(sin^(2)theta+cos^(2)theta)^(3) -3sin^(2)thetacos^(2)theta(sin^(2)theta+cos^(2)theta)]-6[(sin^(2)theta+cos^(2)theta)^(2)-2sin^(2)thetacos^(2)theta]`
`=4[1-3sin^(2)thetacos^(2)theta]-6[1-2sin^(2)thetacos^(2)theta]`
`=4-12sin^(2)thetacos^(2)theta-6+12sin^(2)thetacos^(2)theta=-2`
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