User:Iæfai/Math/SinCos

Given

$$\dfrac{\alpha \sin x + \beta \cos x}{\gamma \sin x + \delta \cos x}$$

Then:

$$\alpha \sin x + \beta \cos x = A(\gamma \sin x + \delta \cos x) + B(\gamma \cos x - \delta \sin x) $$

and:

$$\alpha = A\gamma - B\delta$$

$$\beta = A\delta + B\gamma$$