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.

From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is $${15^ \circ }$$. The distance of the boat from the foot of the light house is