Question : What is $\tan \frac{\theta}{2}$?
Option 1: $\frac{\cos \theta}{1-\sin \theta}$
Option 2: $\frac{\sin \theta}{1-\cos \theta}$
Option 3: $\frac{\cos \theta}{1-\cos \theta}$
Option 4: $\frac{\sin \theta}{1+\cos \theta}$
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Correct Answer: $\frac{\sin \theta}{1+\cos \theta}$
Solution : Given: $\tan\frac{\theta}{2}$ = $\frac{\sin\frac{\theta}{2}}{\cos\frac{\theta}{2}}$ = $\frac{2\sin\frac{\theta}{2}\cos\frac{\theta}{2}}{2\cos^2\frac{\theta}{2}}$ = $\frac{2\sin\frac{\theta}{2}\cos\frac{\theta}{2}}{2\cos^2\frac{\theta}{2}-1 + 1 }$ = $\frac{\sin\theta}{\cos\theta + 1}$ Hence, the correct answer is $\frac{\sin \theta}{\cos\theta + 1}$.
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Question : $\frac{1+\sin \theta}{\cos \theta}$ is equal to which of the following (where $\left.\theta \neq \frac{\pi}{2}\right)?$
Question : Which of the following is equal to $[\frac{\tan \theta+\sec \theta–1}{\tan \theta–\sec \theta+1}]$?
Question : If $\tan\theta=1$, then the value of $\frac{8\sin\theta\:+\:5\cos\theta}{\sin^{3}\theta\:–\:2\cos^{3}\theta\:+\:7\cos\theta}$ is:
Question : Simplify the following expression. $\frac{\sin \theta - 2 \sin ^3 \theta}{2 \cos ^3 \theta - \cos \theta}$
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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