Question

1−cosθ/1+cosθ is equal to

Answer 1

${ \boxed{\boxed{\begin{array}{cc} \rm \: \: given \: \: \frac{1 - cos\theta}{1 + cos\theta} \\ \\\small{\pink{ {\boxed{\begin{array}{cc} \maltese  \bf \: we \: know \: that \\ \\ \bf \to 1 - cos2x = 2 {sin}^{2}x \\ \rm \: so \: \: \: 1 - cosx = 2 {sin}^{2} \frac{x}{2} \\ \\ \rm\: and \\ \\ \bf \to \: 1 + cos2x = 2 {cos}^{2} x \\ \rm \: so \: \: 1 + cosx = 2 {cos}^{2} \frac{x}{2} \end{array}}}}} \\ \\ \bf \: now \\ \\ \rm \frac{1 - cos\theta}{1 + cos\theta} \\ \\ \rm = \frac{2 {sin}^{2} \frac{\theta}{2} }{2 {cos}^{2} \frac{\theta}{2} } \\ \\ \rm = {tan}^{2} \frac{\theta}{2} \end{array}}}}$