`2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)` is equal to

Options

A. 0
B. 3
C. 1
D. `-1`

Answer

D

Explanation

We have,
`2(sin^(6) theta + cos^(6) theta-3) (sin^(4) theta+cos^(4) theta)`
`2[(sin ^(2)theta+cos^(2) theta)^(3) -3 sin^(2) theta cos^(2) theta(sin^(2) theta +cos^(2) theta)] - 3[(sin^(2) theta+cos^(2) theta)^(2) -2 sin^(2) theta cos^(2) theta]`
` =2 (1-3 sin^(2) theta cos^(2) theta) -3 (1-2 sin^(2) theta cos^(2) theta)`
`= 2-6 sin^(2) theta cos^(2) theta -3 +6 sin^(2) theta cos^(2) theta =-1`