operatorname{cosec} 2 theta - cot 2 theta = ? | vedclass

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Question

(A) We know that $\operatorname{cosec} 2 	heta = \frac{1}{\sin 2 	heta}$ and $\cot 2 	heta = \frac{\cos 2 	heta}{\sin 2 	heta}$.Substituting thes

Vedclass · Accepted Answer

$	an 	heta$

Vedclass · Answer

(A) We know that $\operatorname{cosec} 2 	heta = \frac{1}{\sin 2 	heta}$ and $\cot 2 	heta = \frac{\cos 2 	heta}{\sin 2 	heta}$.Substituting these in the expression:$\operatorname{cosec} 2 	heta - \cot 2 	heta = \frac{1}{\sin 2 	heta} - \frac{\cos 2 	heta}{\sin 2 	heta} = \frac{1 - \cos 2 	heta}{\sin 2 	heta}$.Using the trigonometric identities $1 - \cos 2 	heta = 2 \sin^2 	heta$ and $\sin 2 	heta = 2 \sin 	heta \cos 	heta$:$= \frac{2 \sin^2 	heta}{2 \sin 	heta \cos 	heta} = \frac{\sin 	heta}{\cos 	heta} = 	an 	heta$.Thus,the correct option is $A$.

$\operatorname{cosec} 2 \theta - \cot 2 \theta = ?$

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