Question

Cos(5x)cos(2x) + sin(5x)sin(2x)

Answer 1

Use the angle subtraction formula for cosine:

$\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta$

Let

$\alpha=5x$, $\beta=2x$.

Then

$\cos5x\cos2x+\sin5x\sin2x=\cos(5x-2x)=\cos3x$