The sum of solutions of the equation $\frac{\cos x}{1+\sin x}=|\tan 2 x|$,where $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) - \left\{\frac{\pi}{4}, -\frac{\pi}{4}\right\}$,is:

In a $\triangle ABC$,the expression $\frac{a}{\tan A} + \frac{b}{\tan B} + \frac{c}{\tan C}$ is equal to:

In a triangle $ABC$, if $a=7, c=11, \cos A=\frac{17}{22}, \cos C=\frac{1}{14}$, then $b \tan \frac{B}{2} \tan \frac{C-A}{2} =$

Let the angles $A, B, C$ of a triangle $ABC$ be in arithmetic progression. If the exradii $r_1, r_2, r_3$ of triangle $ABC$ satisfy the condition $r_3^2 = r_1 r_2 + r_2 r_3 + r_3 r_1$, then $b =$

If $A$ is the area and $2s$ is the sum of $3$ sides of a triangle,then:

Let $x, y$ and $z$ be positive real numbers. Suppose $x, y$ and $z$ are lengths of the sides of a triangle opposite to its angles $X, Y$ and $Z$,respectively. If $\tan \frac{X}{2} + \tan \frac{Z}{2} = \frac{2y}{x+y+z}$,then which of the following statements is/are $TRUE$?
$(A) 2Y = X + Z$
$(B) Y = X + Z$
$(C) \tan \frac{X}{2} = \frac{x}{y+z}$
$(D) x^2 + z^2 - y^2 = xz$