Equations and results involving double angle formulae

1. I would like to know if this is correct:

$\displaystyle 5sinx-2secx=0$ where x is an element of 0 and 360 (2pi in radians)

$\displaystyle 5sinx-\frac {2}{cosx}=0$

$\displaystyle 5sinxcosx-2=0$

$\displaystyle sin5x-2=0$

$\displaystyle \therefore sinx=\frac {2}{3}, \frac {2}{3} + \pi, \frac {2}{3} + 2\pi$

2. I would like to know where to continue in this question:

$\displaystyle sin3xcosx-cos3xsinx=\frac {\sqrt{3}}{2}$

$\displaystyle 3sinx-4cos^3xcosx-4cos^3x-3cosx=$

$\displaystyle 3sinxcosx-4cos^4x-4sincos^3x-3cos^2xsinx=$

...I don't really know where to go from here and how to find angles for x.

3. I am being introduced to product and sum formulas and I don't know how to tackle the questions.

eg1. $\displaystyle sinx=\frac{3}{2}, 0<x<\frac{\pi}{2}$

Find the exact value of sin2x, cos2x.

The extra formulas given for sinx and cosx are:

$\displaystyle sinx=\frac{2sin\frac{x}{2}}{1+tan^2 \frac{x}{2}}$

and

$\displaystyle cosx=\frac {1-tan^2 \frac{x}{2}}{1+tan^2\frac{x}{2}}$

I know all the normal ones like sin2x=2sinxcosx etc., just not how to apply them.

If you could help me out here that would be great :D