The equation ${\sin ^4}x + {\cos ^4}x + \sin 2x + \alpha = 0$ is solvable for
$ - \frac{1}{2} \le \alpha \le \frac{1}{2}$
$ - 3 \le \alpha \le 1$
$ - \frac{3}{2} \le \alpha \le \frac{1}{2}$
$ - 1 \le \alpha \le 1$
If $2{\cos ^2}x + 3\sin x - 3 = 0,\,\,0 \le x \le {180^o}$, then $x =$
The solution of $tan\,\, 2\theta\,\, tan\theta = 1$ is
Number of solutions of the equation $2^x + x = 2^{sin \ x} + \sin x$ in $[0,10\pi ]$ is -
The number of elements in the set $S=\left\{x \in R : 2 \cos \left(\frac{x^{2}+x}{6}\right)=4^{x}+4^{-x}\right\}$ is$.....$
The number of distinct solutions of the equation $\log _{\frac{1}{2}}|\sin x|=2-\log _{\frac{1}{2}}|\cos x|$ in the interval $[0,2 \pi],$ is