Question

1-cos theta / 1+cos theta​

Answer 1

$\large Method \: 1 \\ \frac{1 - cos \theta}{1 + cos \theta} \\ = \frac{2 {sin}^{2} \frac{ \theta}{2} }{2 {cos}^{2} \frac{ \theta}{2} } \\ = {tan}^{2} \frac{ \theta}{2} \\ \large Method \: 2 \\ \frac{1 - cos \theta}{1 + cos \theta} \\ by \: rationalizing \: denominator \\ \frac{( {1 - cos \theta})^{2} }{1 - {cos}^{2} \theta } \\ = \frac{( {1 - cos \theta})^{2} }{ {sin}^{2} \theta} \\ = ( \frac{1 - cos \theta}{sin \theta} ) ^{2} \\ = ( {cosec \theta - cot \theta})^{2}$