Let $P = \left\{ {\theta :\sin \,\theta - \cos \,\theta = \sqrt 2 \,\cos \,\theta } \right\}$ and $Q = \left\{ {\theta :\sin \,\theta + \cos \,\theta = \sqrt {2\,} \sin \,\theta } \right\}$ be two sets. Then
$P \subset Q$ and $Q - P \ne \phi $
$Q \not\subset P$
$P = Q$
$P \not\subset Q$
If the equation $\cos ^{4} \theta+\sin ^{4} \theta+\lambda=0$ has real solutions for $\theta,$ then $\lambda$ lies in the interval
Number of solutions to the system of equations $sin \frac{x+y}{2}=0$ and $|x| + |y| = 1$
Find the general solution of the equation $\sin 2 x+\cos x=0$
The number of solutions of the equation $2 \theta-\cos ^{2} \theta+\sqrt{2}=0$ is $R$ is equal to
If $x = \frac{{n\pi }}{2}$ , satisfies the equation $sin\, \frac{x}{2}- cos \frac{x}{2} = 1$ $- sin\, x$ & the inequality $\left| {\frac{x}{2}\,\, - \,\,\frac{\pi }{2}} \right|\,\, \le \,\,\frac{{3\pi }}{4}$, then: