The value of theta satisfying the given equat | vedclass

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

Question

(A) Given equation: $\cos 	heta + \sqrt{3} \sin 	heta = 2$. Divide the entire equation by $2$: $\frac{1}{2} \cos 	heta + \frac{\sqrt{3}}{2} \sin

Vedclass · Accepted Answer

$\frac{\pi}{3}$

Vedclass · Answer

(A) Given equation: $\cos 	heta + \sqrt{3} \sin 	heta = 2$. Divide the entire equation by $2$: $\frac{1}{2} \cos 	heta + \frac{\sqrt{3}}{2} \sin 	heta = 1$. Using the identity $\sin(A + B) = \sin A \cos B + \cos A \sin B$,we can rewrite this as: $\sin 	heta \cos \frac{\pi}{3} + \cos 	heta \sin \frac{\pi}{3} = 1$. This simplifies to: $\sin(	heta + \frac{\pi}{3}) = 1$. Since $\sin(\frac{\pi}{2}) = 1$,we have: $	heta + \frac{\pi}{3} = \frac{\pi}{2}$. $	heta = \frac{\pi}{2} - \frac{\pi}{3} = \frac{\pi}{6}$. Wait,checking the options: If $	heta = \frac{\pi}{3}$,then $\cos(\frac{\pi}{3}) + \sqrt{3} \sin(\frac{\pi}{3}) = \frac{1}{2} + \sqrt{3}(\frac{\sqrt{3}}{2}) = \frac{1}{2} + \frac{3}{2} = 2$. Thus,$	heta = \frac{\pi}{3}$ is the correct solution.

The value of $\theta$ satisfying the given equation $\cos \theta + \sqrt{3} \sin \theta = 2$ is:

Similar Questions

The general solution of $1+\sin ^{2} x=3 \sin x \cdot \cos x$,where $\tan x \neq \frac{1}{2}$,is

The smallest positive value of $x$ in degrees satisfying the equation $\tan(x+100^{\circ}) = \tan(x+50^{\circ}) \tan(x) \tan(x-50^{\circ})$ is (in $^{\circ}$)

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

The general solution of the equation $\sqrt{3} \cos \theta + \sin \theta = \sqrt{2}$ is

Find the general solution of the equation $\sin x + \sin 3x + \sin 5x = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module