Question : If $\sec \theta-2 \cos \theta=\frac{7}{2}$, where $\theta$ is a positive acute angle, then the value of $\sec \theta$ is:
Option 1: 6
Option 2: 8
Option 3: 5
Option 4: 4
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Correct Answer: 4
Solution : Given, $\sec \theta-2 \cos \theta=\frac{7}{2}$ We know, $\cos\theta = \frac{1}{\sec\theta}$ ⇒ $\sec \theta-\frac{2}{\sec \theta}=\frac{7}{2}$ ⇒ $(\sec^2\theta - 2)2=7\sec\theta$ ⇒ $2\sec^2\theta - 7\sec\theta -4 = 0$ Solving it as a quadratic equation, using middle-term splitting, ⇒ $2\sec^2\theta - 8\sec\theta + \sec\theta - 4 = 0$ ⇒ $2\sec\theta (\sec\theta-4)+1(\sec\theta - 4) = 0$ ⇒ $(2\sec\theta + 1)(\sec\theta-4)=0$ ⇒ $\sec\theta = -\frac{1}{2}$ and $\sec \theta = 4$ It is given that $\theta$ is an acute angle which means the value $\sec\theta$ should be positive. $\therefore\sec\theta = 4$ Hence, the correct answer is 4.
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Question : If $\sec\theta-\cos\theta=\frac{3}{2}$, where $\theta$ is a positive acute angle, then the value of $\sec\theta$ is:
Question : If $\theta$ is a positive acute angle and $3(\sec^{2}\theta+\tan^{2}\theta)=5$, then the value of $\cos2\theta$ is:
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 $\theta$ is a positive acute angle and $\tan2\theta \tan3\theta=1$, then the value of $2(\cos^2\frac{5\theta}{2}-1)$ is:
Question : If $8 \cot \theta=6$, then the value of $\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta}$ is:
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