Question : What will be the value of $\cos x \operatorname{cosec} x - \sin x \sec x$?
Option 1: $\cot \frac{2x}{2}$
Option 2: $\tan 2 x $
Option 3: $\cot 2 x $
Option 4: $ 2 \cot 2x$
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Correct Answer: $ 2 \cot 2x$
Solution : Given: $\cos x \operatorname{cosec} x – \sin x \sec x$ = $\frac{\cos x}{\sin x} - \frac{\sin x}{\cos x}$ = $\frac{\cos x \cos x - \sin x \sin x}{\cos x \sin x}$ = $\frac{2(\cos^2 x - \sin^2 x)}{2\sin x \cos x}$ = $\frac{2\cos 2x}{\sin 2x}$ = $2 \cot 2x$ Hence, the correct answer is $2\cot 2x$.
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Question : Which of the following is equal to $[\frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{\cos \theta}]$?
Question : The value of $\sqrt{\frac{1+\cos \theta}{1-\cos \theta}}$ is:
Question : $\left(\frac{\tan ^3 \theta}{\sec ^2 \theta}+\frac{\cot ^3 \theta}{\operatorname{cosec}^2 \theta}+2 \sin \theta \cos \theta\right) \div\left(1+\operatorname{cosec}^2 \theta+\tan ^2 \theta\right), 0^{\circ}<\theta<90^{\circ}$, is equal to:
Question : The value of $\sqrt{\frac{1+\cos A}{1-\cos A}}$ is:
Question : $\frac{1+\cos \theta-\sin ^2 \theta}{\sin \theta(1+\cos \theta)} \times \frac{\sqrt{\sec ^2 \theta+\operatorname{cosec}^2 \theta}}{\tan \theta+\cot \theta}, 0^{\circ}<\theta<90^{\circ}$, is equal to:
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