IN-PHASE & QUADRATURE SINUSOIDAL COMPONENTS

Question

I was reading about IN-PHASE & QUADRATURE SINUSOIDAL COMPONENTS. And there is a part I don't understand. Is this part:

Fom trig identity:$$\sin(A+B)=\sin(A)\cos(B)+\cos(A)\sin(B)$$

we have, \begin{align}x(t)&= A\sin(\omega t+\phi)\\ &=A\sin(\phi+\omega t) \\&=[A\sin(\phi)]\cos(\omega t)+[A\cos(\phi)]\sin(\omega t) \\&=A_1\cos(\omega t)+A_2\sin(\omega t)\end{align}

I don't understand how the final equation was obtained.

Answer 1

Just $$A_1=A\sin\phi$$ and $$A_2=A\cos\phi.$$