Question : If $8 \cot \theta=6$, then the value of $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}$ is:
Option 1: 12
Option 2: 7
Option 3: 2
Option 4: 5
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Correct Answer: 7
Solution : $8 \cot \theta = 6$ $\therefore \cot \theta = \frac{6}{8}$ Now, $\frac{(\sin \theta+\cos \theta)}{(\sin \theta-\cos \theta)}$ Dividing numerator and denominator by $\sin \theta$ $=\frac{(1+\cot \theta )}{(1-\cot \theta)}$ $=\frac{1+ \frac{6}{8}}{1- \frac{6}{8}}$ $=\frac{\frac{14}{8}}{\frac{2}{8}}$ $=\frac{14}{2}$ $=7$ Hence, the correct answer is 7.
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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 : If $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}=\frac{3}{2}$, then the value of $\sin ^4 \theta-\cos ^4 \theta$ is:
Question : If $\operatorname{sin} \theta=\frac{4}{5}$, find the value of $\tan \theta-\operatorname{cot} \theta$.
Question : Find the value of the following expression. $5\left(\sin ^4 \theta+\cos ^4 \theta\right)+3\left(\sin ^6 \theta+\cos ^6 \theta\right)+19 \sin ^2 \theta \cos ^2 \theta$
Question : If $\sin\theta+\sin^{2}\theta=1$, then the value of $\cos^{12}\theta+3\cos^{10}\theta+3\cos^{8}\theta+\cos^{6}\theta-1$ is:
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