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Find the value of 6(sin^6theta+cos^6th...

Find the value of `6(sin^6theta+cos^6theta)-9(sin^4theta+cos^4theta)+4`

A

0

B

1

C

`-2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`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]-[1-2sin^(2)thetacos^(2)theta]`
`=4-12sin^(2)thetacos^(2)theta-6+12sin^(2)thetacos ^(2)theta=-2`
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