Questions in trigonometry

Select	Question
	We are given b, c and $\sin B$ such that B is acute and $b
	The sides of triangle are $3x+4y,\ 4x+3y$ and $5x+5y$ units, where $x,\ y>0.$ The triangle is
	In a $\Delta ABC$ $a,\ c,A$ are given and ${{b}_{1}},\ {{b}_{2}}$ are two values of the third side b such that ${{b}_{2}}=2{{b}_{1}}$. Then $\sin A=$
	In a $\Delta ABC$ , $a,\ b,\ A$ are given and ${{c}_{1}},\ {{c}_{2}}$ are two values of the third side c. The sum of the areas of two triangles with sides $a,\ b,\ {{c}_{1}}$ and $a,b,\ {{c}_{2}}$ is
	If in a triangle $ABC$ , $2\cos A=\sin B\,\text{cosec}\,C,$ then
	If the sides of a triangle are $3,\ 5,\ 7,$ then
	If $y=x\tan \frac{\alpha +\beta }{2}$ , then $\tan A+\tan B+\tan C=$
	In a triangle $PQR$ , $\angle R=\frac{\pi }{2}.$ If $\tan \left( \frac{P}{2} \right)$ and $\tan \left( \frac{Q}{2} \right)$ are the roots of the equation $a{{x}^{2}}+bx+c=0(a\ne 0).$ then
	If a triangle $PQR$ , $\sin P,\ \sin Q,\ \sin R$ are in A.P., then
	In a $\Delta ABC,$ if $\frac{\sin A}{\sin C}=\frac{\sin (A-B)}{\sin (B-C)},$ then ${{a}^{2}},\ {{b}^{2}},\ {{c}^{2}}$ are in