trigonometric expressions



I would like to transform trigonometric expressions 
according to my preferred routes. 

E.g.:
 

 a: 2*sin(x)^2-3*cos(x);
 
 to be tranformed by applying the rule cos(x)^2 = 1 - sin(x)^2

 I have unsuccessfully tried trigrat, trigexpand, trigsimp  

 Any hints?

I would also like to solve that equation, by applying given rules.

Thank you 
-- 
Pol