Question

Sin thetha/1+cos thetha+1+cos thetha/sinthetha=2 cosec therha

Answer 1

Answer:

Here is your answer mate! Hope this helps you

Answer 2

Answer :

$\implies \sf \dfrac{ \sin \theta}{1 + \cos\theta} + \dfrac{1 + \cos\theta}{ \sin\theta} = 2 \csc\theta$

By taking LCM

$\implies \sf\frac{ { \sin}^{2}\theta + {(1 + \cos\theta)}^{2} }{(1 + \cos\theta)( \sin\theta)} \\ \\\implies \sf \frac{ { \sin}^{2}\theta +1 +2 \cos \theta +{\cos}^{2} \theta }{(1 + \cos\theta)( \sin\theta)} \\ \\\implies \sf \frac{1 + 1 + 2 \cos \theta }{(1 + \cos\theta)( \sin\theta)} \\ \\\implies \sf \frac{2 + 2 \cos \theta }{(1 + \cos\theta)( \sin\theta)} \\ \\\implies \sf \frac{2( \cancel{1 + \cos \theta}) }{( \cancel{1 + \cos\theta})( \sin\theta)} \\ \\ \implies \sf 2\times\frac{1}{ \sin \theta} \\ \\\implies \sf 2 \times \csc \theta \\ \\ \implies \sf 2 \csc \theta$

LHS = RHS

Hence Proved