The number of values of x in the interval lef | vedclass

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

Question

$x \in\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)$

$14 \operatorname{cosec}^{2} x-2 \sin ^{2} x=21-4 \cos ^{2} x$

$=21-4\left(1-\sin ^{2} x\righ

Vedclass · Accepted Answer

$4$

Vedclass · Answer

$x \in\left(\frac{\pi}{4}, \frac{7 \pi}{4}ight)$

$14 \operatorname{cosec}^{2} x-2 \sin ^{2} x=21-4 \cos ^{2} x$

$=21-4\left(1-\sin ^{2} xight)$

$=17+4 \sin ^{2} x$

$14 \operatorname{cosec} x-6 \sin ^{2} x=17$

let $\sin ^{2} x=p$

$\frac{14}{p}-6 p=17 \Rightarrow 14-6 p^{2}=17 p$

$6 p^{2}+17 p-14=0$

$p=-3.5, \frac{2}{3} \Rightarrow \sin ^{2} x=\frac{2}{3}$

$\Rightarrow \sin x=\pm \sqrt{\frac{2}{3}}$

$	herefore$ Total $4$ solutions

The number of values of $x$ in the interval $\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)$ for which $14 \operatorname{cosec}^{2} x-2 \sin ^{2} x=21$ $-4 \cos ^{2} x$ holds, is

Similar Questions

The general solution of the equation $(\sqrt 3 - 1)\sin \theta + (\sqrt 3 + 1)\cos \theta = 2$ is

Find the general solution of $\cos ec\, x=-2$

The roots of the equation $1 - \cos \theta = \sin \theta .\sin \frac{\theta }{2}$ is

If $2{\cos ^2}x + 3\sin x - 3 = 0,\,\,0 \le x \le {180^o}$, then $x =$

If $e ^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \ldots \infty\right) \log _{e} 2}$ satisfies the equation $t ^{2}-9 t +8=0,$ then the value of $\frac{2 \sin x}{\sin x+\sqrt{3} \cos x}\left(0 < x < \frac{\pi}{2}\right)$ is