Question : The value of $(\frac{1}{\sin\theta}+\frac{1}{\tan\theta})(\frac{1}{\sin\theta}-\frac{1}{\tan\theta})$ is:
Option 1: 0
Option 2: 2
Option 3: 3
Option 4: 1
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Correct Answer: 1
Solution : Given: $(\frac{1}{\sin\theta}+\frac{1}{\tan\theta})(\frac{1}{\sin\theta}-\frac{1}{\tan\theta})$ $= (\operatorname{cosec}\theta+\cot\theta)(\operatorname{cosec}\theta-\cot\theta)$ $=\operatorname{cosec}^2\theta-\cot^2\theta$ $= 1$ Hence, the correct answer is 1.
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Question : If $3 \tan \theta=2 \sqrt{3} \sin \theta, 0^{\circ}<\theta<90^{\circ}$, then the value of $\frac{\operatorname{cosec}^2 2 \theta+\cot ^2 2 \theta}{\sin ^2 \theta+\tan ^2 2 \theta}$ is:
Question : $\frac{1+\sin \theta}{\cos \theta}$ is equal to which of the following (where $\left.\theta \neq \frac{\pi}{2}\right)?$
Question : If $2 \cot \theta = 3$, find the value of $\frac{\sqrt{13} \sin \theta – 3 \tan \theta}{3 \tan \theta + \sqrt{13} \cos \theta}$
Question : If $\sqrt{3} \tan \theta=3 \sin \theta$, then what is the value of $\sin ^2 \theta-\cos ^2 \theta$?
Question : If $\tan \theta=\frac{4}{3}$, then the value of $\frac{3\sin \theta+ 2\cos \theta}{3\sin \theta – 2 \cos \theta}$ is:
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