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the expression (1+sin2alpha)/(cos(2alpha...

the expression `(1+sin2alpha)/(cos(2alpha-2pi)tan(alpha-(3pi)/4))-1/4sin2alpha(cot(alpha/2)+cot((3pi)/2+alpha/2))` simplifies and reduces to

A

1

B

0

C

`sin^(2)(alpha//2)`

D

`sin^(2)alpha`

Text Solution

Verified by Experts

The correct Answer is:
D
`(1+sin 2alpha)/(cos 2alpha.tan((pi)/(4)+alpha))-(sin 2alpha)/(4)[cot.(alpha)/(2)-tan.(alpha)/(2)]`
`=(1+sin 2alpha)/(cos 2alpha.tan((pi)/(4)+alpha))-(sin 2alpha)/(4)[("cos"^(2)(alpha)/(2)-"sin"^(2)(alpha)/(2))/(cos.(alpha)/(2)sin.(alpha)/(2))]`
`=((sin alpha+cos alpha)^(2))/(cos 2alpha((sin alpha+ cos alpha)/(cos alpha - sin alpha)))-cos^(2) alpha`
`= (cos 2 alpha)/(cos 2alpha)-cos^(2)alpha`
`= sin^(2)alpha`
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