Question

How to solve for General Solutions for (2cos^2x=3sinx)

Answer 1

I would replace:
\[\cos^2(x)=1-\sin^2(x)\]
Then you have a quadratic in sin(x) :P So let:
\[\phi = \sin(x) \implies 2(1-\sin^2(x))=3\sin(x) \implies 2(1-\psi^2)=3\psi \implies -2 \psi^2-3\psi+2=0\]
Solve for psi then set psi = sin(x) and you're done :P