Prove the following identities, where the ang | vedclass

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Question

$(\operatorname{cosec} 	heta-\cot 	heta)^{2}=\frac{1-\cos 	heta}{1+\cos 	heta}$

$L.H.S.=(\operatorname{cosec} 	heta-\cot 	heta)^{2}$

$=\le

Vedclass · Accepted Answer

Vedclass · Answer

$(\operatorname{cosec} 	heta-\cot 	heta)^{2}=\frac{1-\cos 	heta}{1+\cos 	heta}$

$L.H.S.=(\operatorname{cosec} 	heta-\cot 	heta)^{2}$

$=\left(\frac{1}{\sin 	heta}-\frac{\cos 	heta}{\sin 	heta}ight)^{2}$

$=\frac{(1-\cos 	heta)^{2}}{(\sin 	heta)^{2}}=\frac{(1-\cos 	heta)^{2}}{\sin ^{2} 	heta}$

$=\frac{(1-\cos 	heta)^{2}}{1-\cos ^{2} 	heta}=\frac{(1-\cos 	heta)^{2}}{(1-\cos 	heta)(1+\cos 	heta)}=\frac{1-\cos 	heta}{1+\cos 	heta}$

$=$ $R.H.S.$

Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

$(\operatorname{cosec} \theta-\cot \theta)^{2}=\frac{1-\cos \theta}{1+\cos \theta}$

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Prove the following identities, where the angles involved are acute angles for which the expressions are defined. $(\operatorname{cosec} \theta-\cot \theta)^{2}=\frac{1-\cos \theta}{1+\cos \theta}$