In $\triangle ABC$,if $\tan A + \tan B + \tan C = 6$ and $\tan A \cdot \tan B = 2$,then $\tan C = \dots$

If in a triangle $ABC,$ $\cos A \cos B + \sin A \sin B \sin C = 1,$ then the sides are proportional to

If $\tan (\pi \cos \theta)=\cot (\pi \sin \theta)$,then a value of $\cos \left(\theta-\frac{\pi}{4}\right)$ among the following is

The angles of depression of the top and the foot of a chimney as seen from the top of a second chimney,which is $150 \, m$ high and standing on the same level as the first,are $\theta$ and $\phi$ respectively. If $\tan \theta = \frac{4}{3}$ and $\tan \phi = \frac{5}{2}$,then the distance between their tops is.......$m$.

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

If $2 \sin x - \cos 2x = 1$,then $(3 - 2 \sin^2 x) = $