If cos(alpha - beta) = 1 and cos(alpha + beta | vedclass

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

Question

(D) Given $\cos(\alpha - \beta) = 1$ and $-\pi < \alpha, \beta < \pi$.Since $-\pi < \alpha < \pi$ and $-\pi < \beta < \pi$,we have $-2\pi < \alpha - \

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Given $\cos(\alpha - \beta) = 1$ and $-\pi Since $-\pi The equation $\cos(\alpha - \beta) = 1$ implies $\alpha - \beta = 0$,so $\alpha = \beta$.Substituting $\alpha = \beta$ into the second equation,we get $\cos(\alpha + \alpha) = \cos(2\alpha) = \frac{1}{e}$.Since $-\pi In the interval $(-2\pi, 2\pi)$,the equation $\cos(2\alpha) = \frac{1}{e}$ has solutions where $\cos(x) = \frac{1}{e}$ for $x \in (-2\pi, 2\pi)$.Since $0 Thus,there are $4$ distinct values for $\alpha$,and since $\alpha = \beta$,there are $4$ ordered pairs $(\alpha, \beta)$.

If $\cos(\alpha - \beta) = 1$ and $\cos(\alpha + \beta) = \frac{1}{e}$,where $-\pi < \alpha, \beta < \pi$,then the total number of ordered pairs $(\alpha, \beta)$ is:

Similar Questions

The solutions of the equation $\sin 2x + \cos 2x = 0$,where $\pi < x < 2\pi$,are

The general value of $\theta$ in the equation $2\sqrt{3} \cos \theta = \tan \theta$ is

If $\sin \theta + \cos \theta = 1$,then the general value of $\theta$ is

Find the principal and general solutions of the equation $\sec x = 2$.

The number of values of $x$ in the interval $[0, 5\pi]$ satisfying the equation $3 \sin^2 x - 7 \sin x + 2 = 0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module