Questions in trigonometry

Select	Question
	The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the sides of the triangle are
	If in a triangle $ABC,$ $\cos A\cos B+\sin A\sin B\sin C=1,$ then the sides are proportional to
	In a $\Delta ABC$ , $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$ and the side $a=2,$ then area of the triangle is
	The perimeter of a $\Delta ABC$ is 6 times the arithmetic mean of the sines of its angles. If the side a is 1, then the angle A is
	Point D, E are taken on the side BC of a triangle $ABC$ such that $BD=DE=EC$.If $\angle BAD=x$ , $\angle DAE=y$ , $\angle EAC=z$ , then the value of $\frac{\sin (x+y)\sin (y+z)}{\sin x\sin z}=$
	If in a $\Delta ABC$ , $\cos A+2\cos B+\cos C=2$ , then$a,b,c$ are in
	If in a $\Delta ABC$ , $\cos 3A+\cos 3B+\cos 3C=1$ , then one angle must be exactly equal to
	ABC is a triangle such that $\sin (2A+B)=$ $\sin (C-A)=$ $-\sin (B+2C)=\frac{1}{2}$. If A, B and C are in A.P., then A, B and C are
	If in the $\Delta ABC,AB=2BC$ , then $\tan \frac{B}{2}:\cot \left( \frac{C-A}{2} \right)$
	In a triangle $ABC$ , if $a=2,B={{60}^{o}}$ and $C={{75}^{o}}$ , then $b =$