The number of solution of the equation $\tan x + \sec x = 2\cos x$ lying in the interval $(0,2\pi )$ is
$0$
$1$
$2$
$3$
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