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Write 2 cos 5x cos 3x as a sum of two cosines.

Contributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Write $2\cos 5x \cos 3x$ as a sum of two cosines. Then find its value at $x = 15^\circ$ to three decimal places.

Need a reminder? The key ideaShow

$\sin C + \sin D = 2\sin\dfrac{C + D}{2}\cos\dfrac{C - D}{2}$ , $\cos C + \cos D = 2\cos\dfrac{C + D}{2}\cos\dfrac{C - D}{2}$ , $\cos C - \cos D = -2\sin\dfrac{C + D}{2}\sin\dfrac{C - D}{2}$ . Products into sums: $2\cos x \cos y = \cos(x + y) + \cos(x - y)$ and so on.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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Write 2 cos 5x cos 3x as a sum of two cosines.

The worked solution

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