Question

Prove that: $\frac{1-cos2\theta +sin2\theta }{1+cos2\theta +sin2\theta }=tan\theta$

Answer 1

L.H.S= $\left(\frac{1-cos2\theta +sin2\theta }{1+cos2\theta +sin2\theta }\right)=\left(\frac{1-(1-2si{n}^2\theta )+2sin\theta cos\theta }{1+(2co{s}^2\theta -1)+2sin\theta cos\theta }\right)=\left(\frac{2sin\theta (sin\theta +cos\theta )}{2cos\theta (cos\theta +sin\theta )}\right)=tan\theta =RHS$