In a triangle $ABC$,if $\cos A \cos B + \sin A \sin B \sin C = 1$,then $\sin A + \sin B + \sin C = $

In a $\triangle ABC$,if $\sin^2 B = \sin A$ and $2 \cos^2 A = 3 \cos^2 B$,then the triangle is

In a triangle $ABC$ with usual notations,if $\tan A, \tan B, \tan C$ are in $H.P.$,then $a^{2}, b^{2}, c^{2}$ are in

If in a triangle $ABC$,$a^2+2bc-(b^2+c^2)=ab \sin \frac{C}{2} \cos \frac{C}{2}$,then $\cot (B+C)=$

In an isosceles triangle $ABC$,$\angle C = \angle A$. If the point of intersection of the bisectors of internal angles $\angle A$ and $\angle C$ divides the median of side $AC$ in the ratio $3 : 1$ (from vertex $B$ to side $AC$),then the value of $\csc \frac{B}{2}$ is equal to

With usual notations in a triangle $ABC$,the product $(I I_1) \cdot (I I_2) \cdot (I I_3)$ has the value equal to