Find the general solution of the equation cos | vedclass

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

Question

(A) Given equation: $\cos 4x = \cos 2x$$\Rightarrow \cos 4x - \cos 2x = 0$Using the formula $\cos A - \cos B = -2 \sin \left(\frac{A+B}{2}\right) \sin

Vedclass · Accepted Answer

$x = \frac{n\pi}{3}$ or $x = n\pi$,$n \in \mathbb{Z}$

Vedclass · Answer

(A) Given equation: $\cos 4x = \cos 2x$$\Rightarrow \cos 4x - \cos 2x = 0$Using the formula $\cos A - \cos B = -2 \sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)$:$-2 \sin \left(\frac{4x+2x}{2}\right) \sin \left(\frac{4x-2x}{2}\right) = 0$$-2 \sin 3x \sin x = 0$$\sin 3x \sin x = 0$This implies $\sin 3x = 0$ or $\sin x = 0$.If $\sin 3x = 0$,then $3x = n\pi \Rightarrow x = \frac{n\pi}{3}$,where $n \in \mathbb{Z}$.If $\sin x = 0$,then $x = n\pi$,where $n \in \mathbb{Z}$.Combining these,the general solution is $x = \frac{n\pi}{3}$ or $x = n\pi$,where $n \in \mathbb{Z}$.

Find the general solution of the equation $\cos 4x = \cos 2x$.

Similar Questions

If $\sqrt{3} \tan 2\theta + \sqrt{3} \tan 3\theta + \tan 2\theta \tan 3\theta = 1$,then the general value of $\theta$ is

If $2\cos^2 x + 3\sin x - 3 = 0$ and $0^\circ \le x \le 180^\circ$,then $x =$

If $\cos x = |\sin x|$,then the general solution is

The general solution of the equation $2 \tan \theta - \cot \theta = -1$ is

The general solution of $4 \sin^2(x) - 4 \sin(x) + 1 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module