Solve using algebraic equation:
5sin2x=3cosx

(no exponents)

by the double angle identity for sine. Move everything to one side and factor out the cosine term.



Now the zero product property tells us that there are two cases where this is true,



In the first equation, cosine becomes zero whenever its argument is an odd integer multiple of , so where

which occurs twice in the interval for and . More generally, if you think of as a point on the unit circle, this occurs whenever also completes a full revolution about the origin. This means for any integer , the general solution in this case would be and .