simplify cos(x - π/2). cos(x - π/2) =

Explanation:

Step1: Use cosine - difference formula

$\cos(A - B)=\cos A\cos B+\sin A\sin B$. Here $A = x$ and $B=\frac{\pi}{2}$, so $\cos(x-\frac{\pi}{2})=\cos x\cos\frac{\pi}{2}+\sin x\sin\frac{\pi}{2}$.

Step2: Evaluate trigonometric values

We know that $\cos\frac{\pi}{2}=0$ and $\sin\frac{\pi}{2}=1$. Substituting these values, we get $\cos x\times0+\sin x\times1$.

Step3: Simplify the expression

$0 + \sin x=\sin x$.

Answer:

$\sin x$