The number of roots of the equation $3\sin^{2}{x = 8\cos x}$ in $\left( \ - \frac{\pi}{2},\frac{\pi}{2} \right)$ is

Question

Dr. Abubacker · Accepted Answer

(a)
Given , $3\sin^{2}{x = 8\cos x}$
$\Rightarrow \ 3(1 - \cos^{2}{x) = 8\cos x}$
$\Rightarrow \ 3\cos^{2}{x - 8\cos{x - 3 = 0}}$
$\Rightarrow \ (3\cos{x + 1)(\cos{x - 3) = 0}}$
$\Rightarrow \ \cos{x = - \frac{1}{3}\ \ \ \ (\because\cos{x 
geq 1)}}$
In the given interval only one value of $x$ is exist

Q. The number of roots of the equation $3\sin^{2}{x = 8\cos x}$ in $\left( \ - \frac{\pi}{2},\frac{\pi}{2} \right)$ is

Explanation

Reviewed by Dr. Abubacker

Want more practice?