The number of solution of the equation,$\sum\limits_{r = 1}^5 {\cos (r\,x)} $ $= 0$ lying in $(0, \pi)$ is :
$2$
$3$
$5$
more than $5$
Number of principal solution of the equation $tan \,3x - tan \,2x - tan\, x = 0$, is
If $\cos \theta = \frac{{ - 1}}{2}$ and ${0^o} < \theta < {360^o}$, then the values of $\theta $ are
If $K = sin^6x + cos^6x$, then $K$ belongs to the interval
For each positive real number $\lambda$. Let $A_\lambda$ be the set of all natural numbers $n$ such that $|\sin (\sqrt{n+1})-\sin (\sqrt{n})|<\lambda$. Let $A_\lambda^c$ be the complement of $A_\lambda$ in the set of all natural numbers. Then,
If $4{\sin ^4}x + {\cos ^4}x = 1,$ then $x =$