If `x=(2sintheta)/(1+costheta+sintheta),t h e n(1-costheta+sintheta)/(1+sintheta)` is equal to

Options

A. 1+x
B. 1-x
C. x
D. `1/x`

Answer

C

Explanation

Multiplying the numerator ans denominator of x by
`1-costheta+sintheta`,we get
`x=(2sintheta(1-costheta+sintheta))/((1+sintheta)^2-cos^2theta)`
`=(2sintheta(1-costheta+sintheta))/((1+sintheta)^2-(1-sin^2theta))`
`=(2sintheta.(1-costheta+sintheta))/((1+sintheta)(2sintheta))`
`=(1-costheta+sintheta)/(1+sintheta)`