The number of roots of the equation $\cos ^7 \theta-\sin ^4 \theta=1$ that lie in the interval $[0,2 \pi]$ is
$2$
$3$
$4$
$8$
If $\cos \,x = \frac{{2\cos y - 1}}{{2 - \cos y}},x,\,y\, \in \,\left( {0,\pi } \right),$ then $tan(x/2)cot(y/2) =$
Let $A=\left\{\theta \in R:\left(\frac{1}{3} \sin \theta+\frac{2}{3} \cos \theta\right)^2=\frac{1}{3} \sin ^2 \theta+\frac{2}{3} \cos ^2 \theta\right\}$.Then
If $cosx + secx =\, -2$, then for a $+ve$ integer $n$, $cos^n x + sec^n x$ is
If $tanA + cotA = 4$, then $tan^4A + cot^4A$ is equal to
The solution set of the equation $tan(\pi\, tanx) = cot(\pi\, cot\, x)$ is