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Options

A. 0
B. 1
C. 3
D. sin `4alpha + cos6alpha`

Answer

B

Explanation

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