If $A + B + C = \pi $ and $\cos A = \cos B\,\cos C,$ then $\tan B\,\,\tan C$ is equal to

The value of the expression $1 - \frac{{{{\sin }^2}y}}{{1 + \cos \,y}} + \frac{{1 + \cos \,y}}{{\sin \,y}} - \frac{{\sin \,\,y}}{{1 - \cos \,y}}$ is equal to

Find the value of $\cos \left(-1710^{\circ}\right)$.

In a right angled triangle the hypotenuse is $2 \sqrt 2$ times the perpendicular drawn from the opposite vertex. Then the other acute angles of the triangle are

Which of the following is correct

If $x\sin 45^\circ {\cos ^2}60^\circ = \frac{{{{\tan }^2}60^\circ {\rm{cosec}}30^\circ }}{{\sec 45^\circ {{\cot }^2}30^\circ }},$ then $x = $