Question

write the expression as the sine or cosine of an angle.
cos\frac{\pi}{7}cosx - sin\frac{\pi}{7}sinx
?(x\square\frac{\pi}{7})
hint: sin(a \pm b)=sinacosb \pm cosasinb
cos(a \pm b)=cosacosb \mp sinasinb

Explanation:

Step1: Recall the cosine addition formula

The formula for \(\cos(A + B)=\cos A\cos B-\sin A\sin B\).

Step2: Identify \(A\) and \(B\)

In the given expression \(\cos\frac{\pi}{7}\cos x-\sin\frac{\pi}{7}\sin x\), let \(A = x\) and \(B=\frac{\pi}{7}\).
Then, by the formula \(\cos(A + B)=\cos A\cos B-\sin A\sin B\), we have \(\cos(x+\frac{\pi}{7})\)

Answer:

\(\cos(x +\frac{\pi}{7})\)