The cosine difference formula yields
[tex]\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)[/tex]
In your case,
[tex]a=\dfrac{\pi}{2},\quad b=x[/tex]
so the formula translates to
[tex]\cos\left(\dfrac{\pi}{2}-x\right)=\cos\left(\dfrac{\pi}{2}\right)\cos(x)+\sin\left(\dfrac{\pi}{2}\right)\sin(x)[/tex]
Since
[tex]\cos\left(\dfrac{\pi}{2}\right)=0,\quad \sin\left(\dfrac{\pi}{2}\right)=1[/tex]
the expression above becomes
[tex]0\cdot\cos(x)+1\cdot\sin(x)=\sin(x)[/tex]
