The solution of $tan\,\, 2\theta\,\, tan\theta = 1$ is
$\frac{\pi }{3}$
$(6n \pm 1)\frac{\pi }{6}$
$(4n \pm 1)\frac{\pi }{6}$
$(2n \pm 1)\frac{\pi }{6}$
The number of solutions of the equation $2 \theta-\cos ^{2} \theta+\sqrt{2}=0$ is $R$ is equal to
If $sin^2x + sinx \,cosx -6cos^2x = 0$ and $-\frac{\pi}{2} < x < 0$, then the value of $cos2x$, is
The general solution of $\sin x - \cos x = \sqrt 2 $, for any integer $n$ is
The number of solution of the equation $2\cos ({e^x}) = {5^x} + {5^{ - x}}$, are
Statement $-1:$ The number of common solutions of the trigonometric equations $2\,sin^2\,\theta - cos\,2\theta = 0$ and $2 \,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, 2\pi ]$ is two.
Statement $-2:$ The number of solutions of the equation, $2\,cos^2\,\theta - 3\,sin\,\theta = 0$ in the interval $[0, \pi ]$ is two.