Question

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

Answer 1

`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`