Question

assignment 7.2: sum and difference identities
score: 50/100 answered: 3/6
question 4
simplify sin(x - \frac{\pi}{2}) to a single trig function using a sum or difference of angles identity.
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Explanation:

Step1: Recall the difference - of - angles formula

The formula for $\sin(A - B)=\sin A\cos B-\cos A\sin B$. Here, $A = x$ and $B=\frac{\pi}{2}$.
So, $\sin(x-\frac{\pi}{2})=\sin x\cos\frac{\pi}{2}-\cos x\sin\frac{\pi}{2}$.

Step2: Evaluate trigonometric values

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

Step3: Simplify the expression

$\sin x\times0-\cos x\times1=-\cos x$.

Answer:

$-\cos x$