Questions in trigonometry

Select	Question
	If $(2\cos x-1)(3+2\cos x)=0,\,0\le x\le 2\pi $, then $x=$
	If $0\le x\le \pi $and ${{81}^{{{\sin }^{2}}x}}+{{81}^{{{\cos }^{2}}x}}=30$, then x =
	If $\sin \theta =\sqrt{3}\cos \theta ,-\pi <\theta <0$, then $\theta =$
	The value of $\theta $ in between ${{0}^{o}}$and ${{360}^{o}}$and satisfying the equation $\tan \theta +\frac{1}{\sqrt{3}}=0$is equal to
	The solution of equation ${{\cos }^{2}}\theta +\sin \theta +1=0$ lies in the interval
	The number of solution of the equation $2\cos ({{e}^{x}})={{5}^{x}}+{{5}^{-x}}$, are
	The most general value of $\theta $satisfying the equations $\tan \theta =-1$ and $\cos \theta =\frac{1}{\sqrt{2}}$is
	The most general value of $\theta $which will satisfy both the equations $\sin \theta =-\frac{1}{2}$and $\tan \theta =\frac{1}{\sqrt{3}}$is
	Common roots of the equations $2{{\sin }^{2}}x+{{\sin }^{2}}2x=2$ and $\sin 2x+\cos 2x=\tan x,$ are
	If $r\,\sin \theta =3,r=4(1+\sin \theta ),\,\,0\le \theta \le 2\pi ,$then $\theta =$