Question

sin 3 A ÷ cos2A < 0 lies in

Answer 1

sin3A = cos2A 
sin3A = sin(90- 2A) 
Cancelling sin from both sides.We get, 
3A = 90 - 2A 
5A = 90 
therefore A = 90/5 = 18 degrees. 

If you ask why did i change cosA on the RHS to sin(90-2A)....I used the identity cosA = sin(90-A). 
If you ask why did i cancel sin then i'll say sin3A is not sin of angle 3A and it is not to be confused with sinA because sinA is sin of angle A and sin3A is three times sin of angle A or Sin * 3A.