Prove that,frac{sin theta}{1+cos theta}+frac{ | vedclass

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(N/A) $L$.$H$.$S$. $= \frac{\sin 	heta}{1+\cos 	heta} + \frac{1+\cos 	heta}{\sin 	heta}$$= \frac{\sin^2 	heta + (1+\cos 	heta)^2}{\sin 	heta(1+

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(N/A) $L$.$H$.$S$. $= \frac{\sin 	heta}{1+\cos 	heta} + \frac{1+\cos 	heta}{\sin 	heta}$$= \frac{\sin^2 	heta + (1+\cos 	heta)^2}{\sin 	heta(1+\cos 	heta)}$$= \frac{\sin^2 	heta + 1 + \cos^2 	heta + 2 \cos 	heta}{\sin 	heta(1+\cos 	heta)}$ $\quad [\because (a+b)^2 = a^2 + b^2 + 2ab]$$= \frac{(\sin^2 	heta + \cos^2 	heta) + 1 + 2 \cos 	heta}{\sin 	heta(1+\cos 	heta)}$$= \frac{1 + 1 + 2 \cos 	heta}{\sin 	heta(1+\cos 	heta)}$ $\quad [\because \sin^2 	heta + \cos^2 	heta = 1]$$= \frac{2 + 2 \cos 	heta}{\sin 	heta(1+\cos 	heta)}$$= \frac{2(1+\cos 	heta)}{\sin 	heta(1+\cos 	heta)}$$= \frac{2}{\sin 	heta} = 2 \operatorname{cosec} 	heta = 	ext{R.H.S.}$ $\quad [\because \operatorname{cosec} 	heta = \frac{1}{\sin 	heta}]$

Prove that,
$\frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}=2 \operatorname{cosec} \theta$

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Prove that,$\frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}=2 \operatorname{cosec} \theta$