When solving $\sin^2 x = \frac14(2+ \sqrt 3)$, is it better to substitute $\sin^2x=1-\cos^2x$ or $\sin^2x=\frac12(1-\cos 2 x)?$ I am trying to evaluate
$$\sin^2 x = \frac{2+ \sqrt 3}{4}$$ where $x$ is $0$ to $2 \pi$.
For $ \sin^2 x$, I can substitute it to either:

*

*$ 1 - \cos ^2 x$ (Pythagorean identity)


*$ \frac12( 1 - \cos 2 x)$ (double angle formula)
How do I know which formula to use for this evaluation?

$$\frac{2+\sqrt 3}{4} = \sin^2x = \frac{1-\cos 2x}{2},$$
$$\cos 2x = 1-\frac{2+\sqrt 3}{2} = -\frac{\sqrt 3}{2}.$$
