If $K = sin^6x + cos^6x$, then $K$ belongs to the interval
$\left[ {\frac{7}{8},\frac{5}{4}} \right]$
$\left[ {\frac{1}{5},\frac{5}{8}} \right]$
$\left[ {\frac{1}{4},1} \right]$
None of these
The number of distinct solutions of the equation $\frac{5}{4} \cos ^2 2 x+\cos ^4 x+\sin ^4 x+\cos ^6 x+\sin ^6 x=2$ in the interval $[0,2 \pi]$ is
Number of solutions of the equation $2^x + x = 2^{sin \ x} + \sin x$ in $[0,10\pi ]$ is -
The general value of $\theta $satisfying the equation $2{\sin ^2}\theta - 3\sin \theta - 2 = 0$ is
Let $S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }$ If $T =\sum_{\theta \in S } \cos 2 \theta$, then $T + n ( S )$ is equal
If $(1 + \tan \theta )(1 + \tan \phi ) = 2$, then $\theta + \phi =$ ....$^o$