Question

Prove LHS=RHS plz help me out​

Answer 1

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Answer 2

To Prove :

$\frac{ \sin\theta }{1 + \cos\theta} + \frac{1 + \cos\theta}{ \sin\theta } = 2 cosec\theta$

Proof :

→ LHS

→ $\frac{ \sin\theta }{1 + \cos\theta } + \frac{1 + \cos\theta }{ \sin\theta }$

→ $\frac{ { \sin }^{2} \theta + { (1 + \cos\theta)}^{2} }{(1 + \cos\theta)( \sin\theta) }$

→ $\frac{ \sin ^{2} \theta + 1 + \cos ^{2} \theta + 2 \cos\theta }{ \sin\theta + \cos\theta .\sin\theta }$

→ $\frac{2(1 + \cos\theta) }{( \sin\theta)(1 + \cos\theta) }$

→$\frac{2}{ \sin\theta}$

→$2 \: \: cosec \: \theta$

→ RHS

Hence, proved.