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

In $\triangle ABC$,if $\cos A \cdot \cos B \cdot \cos C = \frac{1}{5}$,then $\tan A \tan B + \tan B \tan C + \tan C \tan A = $

In a triangle $PQR$,$P$ is the largest angle and $\cos P = \frac{1}{3}$. Further,the incircle of the triangle touches the sides $PQ, QR$ and $RP$ at $N, L$ and $M$ respectively,such that the lengths of $PN, QL$ and $RM$ are consecutive even integers. Then the possible length$(s)$ of the side$(s)$ of the triangle is (are):
$(A) 16$
$(B) 18$
$(C) 24$
$(D) 22$

If $7 \cos \theta - \sin \theta = 5$ and $\tan \theta > 0$,then $\tan \theta =$

The value of $\theta$,satisfying both the equations $\cos \theta = \frac{1}{\sqrt{2}}$ and $\tan \theta = -1$ in the interval $[0, 2\pi]$,is

Let in a right-angled triangle,the smallest angle be $\theta$. If a triangle formed by taking the reciprocal of its sides is also a right-angled triangle,then $\sin \theta$ is equal to: