The general solution of cos 4theta = cos 3the | vedclass

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

Question

(A) Given equation: $\cos 4	heta = \cos 3	heta$.Using the general solution formula for $\cos x = \cos y$, which is $x = 2n\pi \pm y$ where $n \in \m

Vedclass · Accepted Answer

$2n\pi \pm \frac{2n\pi}{7}, n \in \mathbb{Z}$

Vedclass · Answer

(A) Given equation: $\cos 4	heta = \cos 3	heta$.Using the general solution formula for $\cos x = \cos y$, which is $x = 2n\pi \pm y$ where $n \in \mathbb{Z}$.Here, $x = 4	heta$ and $y = 3	heta$.Case $1$: $4	heta = 2n\pi + 3	heta \implies 	heta = 2n\pi$.Case $2$: $4	heta = 2n\pi - 3	heta \implies 7	heta = 2n\pi \implies 	heta = \frac{2n\pi}{7}$.Thus, the general solution is $	heta = 2n\pi$ or $	heta = \frac{2n\pi}{7}$ for $n \in \mathbb{Z}$.

The general solution of $\cos 4\theta = \cos 3\theta$ is $\theta =.....$

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 $\theta \in [-2 \pi, 2 \pi]$,then the number of solutions of $2 \sqrt{2} \cos^2 \theta + (2 - \sqrt{6}) \cos \theta - \sqrt{3} = 0$ is equal to:

Let $x \in [0, 6\pi]$ satisfy the equation $\cos x - \sin x = -1$. If $x = k(\frac{\pi}{3})$ where $k \in \mathbb{N}$, then find the number of possible values of $k$.

Let $X = \{x \in \mathbb{R} : \cos(\sin x) = \sin(\cos x)\}$. The number of elements in $X$ is

If ${\left( {\frac{{\sin \theta }}{{\sin \phi }}} \right)^2} = \frac{{\tan \theta }}{{\tan \phi }} = 3,$ then the values of $\theta$ and $\phi$ are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module