The larger of $$\cos \left( {In\,\,\theta } \right)$$ and $$In $$ $$\left( {\cos \,\,\theta } \right)$$ If $${e^{ - \pi /2}} < \theta < {\pi \over 2}$$ is ..................

Find all the solution of $$4$$ $${\cos ^2}x\sin x - 2{\sin ^2}x = 3\sin x$$

If $$\tan \,A = \left( {1 - \cos B} \right)/\sin B,$$ then $$tan2A = tan\,B$$.

The ex-radii $${r_1},{r_2},{r_3}$$ of $$\Delta $$$$ABC$$ are H.P. Show that its sides $$a, b, c$$ are in A.P.