Correct Answer - 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`