If tan x = frac{3}{4} and pi

Question

(D) Given $	an x = \frac{3}{4}$ and $\pi < x < \frac{3 \pi}{2}$.Since $x$ is in the third quadrant,$\sec^2 x = 1 + 	an^2 x = 1 + \frac{9}{16} = \fra

Vedclass · Accepted Answer

$\frac{-1}{\sqrt{10}}$

Vedclass · Answer

(D) Given $	an x = \frac{3}{4}$ and $\pi Since $x$ is in the third quadrant,$\sec^2 x = 1 + 	an^2 x = 1 + \frac{9}{16} = \frac{25}{16}$.Thus,$\sec x = -\frac{5}{4}$ (as $\sec x Given $\pi In the interval $(\frac{\pi}{2}, \frac{3 \pi}{4})$,$\cos \frac{x}{2}$ is negative.Using the half-angle formula,$\cos \frac{x}{2} = -\sqrt{\frac{1 + \cos x}{2}}$.Substituting $\cos x = -\frac{4}{5}$,we get $\cos \frac{x}{2} = -\sqrt{\frac{1 - 4/5}{2}} = -\sqrt{\frac{1/5}{2}} = -\sqrt{\frac{1}{10}} = -\frac{1}{\sqrt{10}}$.

If $\tan x = \frac{3}{4}$ and $\pi < x < \frac{3 \pi}{2}$,then $\cos \frac{x}{2} = . . . . . .$

Similar Questions

If $\frac{\tan 3A}{\tan A} = a$,then $\frac{\sin 3A}{\sin A}$ is equal to

If $3 \sin 2 \theta = 2 \sin 3 \theta$ and $0 < \theta < \pi$,then the value of $\sin \theta$ is equal to

If $\tan \theta + \tan \left(\theta + \frac{\pi}{3}\right) + \tan \left(\theta + \frac{2\pi}{3}\right) = 3$,then which of the following is equal to $1$?

$\tan 20^\circ \cot 10^\circ \cot 50^\circ$ is equal to

$96 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33}$ is equal to $......$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module