If tan theta = frac{1}{sqrt{11}} and 0

Question

(C) Given $	an 	heta = \frac{1}{\sqrt{11}}.$We know that $\sec^{2} 	heta = 1 + 	an^{2} 	heta = 1 + \frac{1}{11} = \frac{12}{11}.$Also,$\operatorn

Vedclass · Accepted Answer

$\frac{5}{6}$

Vedclass · Answer

(C) Given $	an 	heta = \frac{1}{\sqrt{11}}.$We know that $\sec^{2} 	heta = 1 + 	an^{2} 	heta = 1 + \frac{1}{11} = \frac{12}{11}.$Also,$\operatorname{cosec}^{2} 	heta = 1 + \cot^{2} 	heta = 1 + (\frac{1}{	an 	heta})^{2} = 1 + (\sqrt{11})^{2} = 1 + 11 = 12.$Now,substitute these values into the expression:$\frac{\operatorname{cosec}^{2} 	heta - \sec ^{2} 	heta}{\operatorname{cosec}^{2} 	heta + \sec ^{2} 	heta} = \frac{12 - \frac{12}{11}}{12 + \frac{12}{11}}.$Divide the numerator and denominator by $12$:$\frac{1 - \frac{1}{11}}{1 + \frac{1}{11}} = \frac{\frac{10}{11}}{\frac{12}{11}} = \frac{10}{12} = \frac{5}{6}.$

If $\tan \theta = \frac{1}{\sqrt{11}}$ and $0 < \theta < \frac{\pi}{2},$ then the value of $\frac{\operatorname{cosec}^{2} \theta - \sec ^{2} \theta}{\operatorname{cosec}^{2} \theta + \sec ^{2} \theta}$ is

Similar Questions

If $\tan A = 2\tan B + \cot B,$ then $2\tan (A - B) = $

If $3\cos \theta + 4\sin \theta = 5$,then the value of $3\sin \theta - 4\cos \theta$ is:

If $\sin \alpha = -\frac{3}{5},$ where $\pi < \alpha < \frac{3\pi}{2},$ then $\cos \frac{\alpha}{2} = $

If $\alpha$ is a root of $25\cos^2\theta + 5\cos\theta - 12 = 0$ and $\pi/2 < \alpha < \pi$,then $\sin 2\alpha$ is equal to

$\frac{\sec 8A - 1}{\sec 4A - 1} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module