Question

plz answer..i need help fast

Answer 1

$\bold{ \: to \: prove :} \: \: \frac{ \sin\theta}{1 - \cos\theta } \: = cosec \theta \: + \cot \theta$



LHS ,

$\frac{ \sin \theta }{1 - cos \theta}$


$\mathbf{ \underline{Multiply \: and \: Divide \: by } \: ( 1 + cos \theta ) , }$



$= > \frac{(sin \theta)( \: 1 + \: cos \theta)}{(1 - cos \theta)(1 + cos \theta)} \\ \\ \\ \\ = > \frac{sin \theta \: + sin \theta \: cos \theta}{1 - {cos}^{2} \theta} \\ \\ \\ \\ = > \frac{sin \theta \: + sin \theta \: cos \theta \: }{sin ^{2} \theta} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ | \: 1 - {cos}^{2} \theta \: = {sin}^{2} \theta} \\ \\ \\ \\ = > \frac{ \sin \theta}{ {sin}^{2} \theta} + \frac{ \sin \theta \: \cos \theta }{ {sin}^{2} \theta } \\ \\ \\ \\ = > \frac{1}{sin \theta} + \frac{cos \theta}{ \sin \theta} \\ \\ \\ \\ = > cosec \theta \: + cot \theta \\ \\ \\ \\ \\ \\ \\ \boxed{\bold{ \underline{hence \: proved.}}}$