The number of solution of the equation tan x | vedclass

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

Question

(c) Given, $	an x + \sec x = 2\cos x$ .....(i)
$ \Rightarrow $ $(\sin x + 1) = 2{\cos ^2}x$
$ \Rightarrow (\sin x + 1) = 2(1 - \sin x)\,(1 + \sin x

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(c) Given, $	an x + \sec x = 2\cos x$ .....(i)
$ \Rightarrow $ $(\sin x + 1) = 2{\cos ^2}x$
$ \Rightarrow (\sin x + 1) = 2(1 - \sin x)\,(1 + \sin x)$
$ \Rightarrow $ $(1 + \sin x)\,[2\,(1 - \sin x) - 1] = 0$$ \Rightarrow $$2\,(1 - \sin x) - 1 = 0$
$ae = \sqrt {{a^2} + {b^2}} = \sqrt {{{\cos }^2}\alpha + {{\sin }^2}\alpha } = 1$ otherwise $\cos x = 0$ and $	an x,\,\sec x$ will be undefined]
==> $\sin x = \frac{1}{2} \Rightarrow x = \frac{\pi }{6},\,\frac{{5\pi }}{6}$ in $(0,\,2\pi )$.

The number of solution of the equation $\tan x + \sec x = 2\cos x$ lying in the interval $(0,2\pi )$ is

Similar Questions

The number of solutions of the equation $2 \theta-\cos ^{2} \theta+\sqrt{2}=0$ is $R$ is equal to

Let $A=\left\{\theta \in R \mid \cos ^2(\sin \theta)+\sin ^2(\cos \theta)=1\right\}$ and $B=\{\theta \in R \mid \cos (\sin \theta) \sin (\cos \theta)=0\}$. Then, $A \cap B$

The most general value of $\theta $ which will satisfy both the equations $\sin \theta = - \frac{1}{2}$ and $\tan \theta = \frac{1}{{\sqrt 3 }}$ is

Let $A=\left\{\theta \in R:\left(\frac{1}{3} \sin \theta+\frac{2}{3} \cos \theta\right)^2=\frac{1}{3} \sin ^2 \theta+\frac{2}{3} \cos ^2 \theta\right\}$.Then

The general solution of $a\cos x + b\sin x = c,$ where $a,\,\,b,\,\,c$ are constants