If 2 cos^{2} theta + 3 cos theta = 2,then the | vedclass

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

Question

(C) Given the equation: $2 \cos^{2} 	heta + 3 \cos 	heta = 2$ Rearranging the terms: $2 \cos^{2} 	heta + 3 \cos 	heta - 2 = 0$ Factoring the quadr

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(C) Given the equation: $2 \cos^{2} 	heta + 3 \cos 	heta = 2$ Rearranging the terms: $2 \cos^{2} 	heta + 3 \cos 	heta - 2 = 0$ Factoring the quadratic equation: $2 \cos^{2} 	heta + 4 \cos 	heta - \cos 	heta - 2 = 0$ $2 \cos 	heta(\cos 	heta + 2) - 1(\cos 	heta + 2) = 0$ $(2 \cos 	heta - 1)(\cos 	heta + 2) = 0$ This gives two possible values: $\cos 	heta = \frac{1}{2}$ or $\cos 	heta = -2$ Since the range of the cosine function is $[-1, 1]$,the value $\cos 	heta = -2$ is not possible. Therefore,the permissible value is $\cos 	heta = \frac{1}{2}$.

If $2 \cos^{2} \theta + 3 \cos \theta = 2$,then the permissible value of $\cos \theta$ is

Similar Questions

Solve $\tan 2x = -\cot \left(x + \frac{\pi}{3}\right)$

The number of solutions of the equation $\sec x \cos 5x + 1 = 0$ in the interval $[0, 2\pi]$ is

If $m$ and $n$ respectively are the numbers of positive and negative values of $\theta$ in the interval $[-\pi, \pi]$ that satisfy the equation $\cos 2 \theta \cos \frac{\theta}{2} = \cos 3 \theta \cos \frac{9 \theta}{2}$,then $mn$ is equal to $.............$.

The equation $\sqrt{3} \sin x + \cos x = 4$ has

The number of distinct solutions of $\sec \theta + \tan \theta = \sqrt{3}$ for $0 \leqslant \theta \leqslant 2\pi$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module