Question

Can someone please help me?

Write the expression as either the sine, cosine, or tangent of a single angle.

cos(pi/3)cos(pi/5)+sin(pi/3)sin(pi/5)

Answer 1

Use this trig identity:\[
\cos(x-y) = \cos(x)\cos(y) + \sin(x)\sin(y)
\]Identify \(x\) and \(y\).

Answer 2

would it be (5pi/15 - 3pi/15) = cos (2 pi/15)?

Answer 3

Yes.

http://www.wolframalpha.com/input/?i=%5Bcos%28pi%2F3%29cos%28pi%2F5%29%2Bsin%28pi%2F3%29sin%28pi%2F5%29%5D+-+%5Bcos+%282+pi%2F15%29%5D

If you subtract them, you get 0, which means they are equal.

Answer 4

so the answer to the question is (5pi/15 - 3pi/15) = cos (2 pi/15)

Answer 5

The whole answer is:
\[\begin{split}
\cos(\pi/3)\cos(\pi/5)+\sin(\pi/3)\sin(\pi/5) &= \cos(\pi / 3 - \pi/5) \\
&= \cos(5\pi / 15 - 3\pi/15) \\
&= \cos(2\pi /15)
\end{split}
\]

Answer 6

oh okay thank you for your help!