If tan (cot x) = cot (tan x), then sin 2x = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the equation: $	an (\cot x) = \cot (	an x)$Using the identity $\cot 	heta = 	an (\frac{\pi}{2} - 	heta)$,we have:$	an (\cot x) = 	an

Vedclass · Accepted Answer

$\frac{4}{(2n + 1)\pi}$

Vedclass · Answer

(B) Given the equation: $	an (\cot x) = \cot (	an x)$Using the identity $\cot 	heta = 	an (\frac{\pi}{2} - 	heta)$,we have:$	an (\cot x) = 	an (\frac{\pi}{2} - 	an x)$The general solution for $	an \alpha = 	an \beta$ is $\alpha = n\pi + \beta$,where $n \in \mathbb{Z}$.Thus,$\cot x = n\pi + \frac{\pi}{2} - 	an x$Rearranging the terms:$\cot x + 	an x = n\pi + \frac{\pi}{2}$Using the identity $	an x + \cot x = \frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} = \frac{\sin^2 x + \cos^2 x}{\sin x \cos x} = \frac{1}{\frac{1}{2} \sin 2x} = \frac{2}{\sin 2x}$:$\frac{2}{\sin 2x} = n\pi + \frac{\pi}{2} = \frac{(2n + 1)\pi}{2}$Solving for $\sin 2x$:$\sin 2x = \frac{4}{(2n + 1)\pi}$

If $\tan (\cot x) = \cot (\tan x),$ then $\sin 2x =$

Similar Questions

The number of solutions of the equation $2x + 3 \tan x = \pi$,where $x \in [-2\pi, 2\pi] - \left\{ \pm \frac{\pi}{2}, \pm \frac{3\pi}{2} \right\}$,is

The number of solutions of the equation $\tan x + \sec x = 2 \cos x$ lying in the interval $[0, 2 \pi]$ is

The number of solutions of $\cos 2 \theta = \sin \theta$ in the interval $(0, 2 \pi)$ is:

The general solution of the trigonometric equation $\tan x + \tan 2x + \tan 3x = \tan x \cdot \tan 2x \cdot \tan 3x$ is

The number of solutions of $\tan(5\pi \cos \theta) = \cot(5\pi \sin \theta)$ for $\theta$ in $(0, 2\pi)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module