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
Let $X=\{x \in R: \cos (\sin x)=\sin (\cos x)\} .$ The number of elements in $X$ is
If $\sin (A + B) =1 $ and $\cos (A - B) = \frac{{\sqrt 3 }}{2},$ then the smallest positive values of $A$ and $ B$ are
The number of values of $\theta$ in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ such that $\theta \neq \frac{n \pi}{5}$ for $n=0, \pm 1, \pm 2$ and $\tan \theta=\cot 5 \theta$ as well as $\sin 2 \theta=\cos 4 \theta$ is
$\sum\limits_{r = 1}^{100} {\frac{{\tan \,{2^{r - 1}}}}{{\cos \,{2^r}}}} $ is equal to
Find the general solution of the equation $\cos 4 x=\cos 2 x$