The expression `3{sin^4((3pi/2)-alpha)+sin^4(3pi-alpha)} -2{sin^6(pi/2+alpha)+sin^6(5pi-alpha)}` is equal to

Options

A. 0
B. 1
C. 3
D. None of these

Answer

B

Explanation

`3[sin^4(3/2pi-alpha)+sin^4(3pi+alpha)]`
`-2[sin^6(1/2pi-alpha)+sin^6(5pi-alpha)]`
`=3(cos^4alpha+sin^4alpha)-2(cos^6alpha+sin^6alpha)`
`3(1-2sin^2alphacos^2alpha)-2[(sin^2alpha+cos^2alpha)^3`
`-3sin^2alphacos^2alpha(sin^2alpha+cos^2alpha)]`
`=3(1-2sin^2alphacos^2alpha)-2[1-3sin^2alphacos^2alpha]`
=1