Prove that: `(1+sintheta-costheta)/(1+sintheta+costheta)=tan(theta/2)`

Explanation

`sin theta=frac{2 tan frac{theta}{2}}{1+tan ^{2} frac{theta}{2}}`


`cos theta=frac{1-tan ^{2} frac{theta}{2}}{1+tan ^{2} frac{theta}{2}}`


Substituting this in the above equation we get, `frac{1+tan ^{2} frac{theta}{2}+2 tan frac{theta}{2}-1+tan ^{2} frac{theta}{2}}{1+tan ^{2} frac{theta}{2}+2 tan frac{theta}{2}+1-tan ^{2} frac{theta}{2}}`


`Rightarrow frac{2 tan frac{theta}{2}+2 tan ^{2} frac{theta}{2}}{2+2 tan frac{theta}{2}}=tan frac{theta}{2}`