Question

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

Answer 1

\[\cos((π)/(5))\cos((π)/(7))+\sin((π)/(5))\sin((π)/(7))\]

Answer 2

doesn't that look like the cosine of the difference of two angles?
See http://www.intmath.com/analytic-trigonometry/2-sum-difference-angles.php

Answer 3

how does that help with the problem?

Answer 4

the formula is
cos(a+b) = cos(a) cos(b) - sin(a) sin(b)

if they give you the stuff on the right, then you know you can replace it with the stuff on the left, which is cos(a+b)

I would match the a's and b's in the formula with your angles
once you figure out what a and b are, add them up, and put the sum inside a cosine

Answer 5

... so cos(2π)/(65) - sin(2π)/(65) ?

Answer 6

First, let me write the correct formula. your expression is
\[ \cos(π/5)\cos(π/7)+\sin(π/5)\sin(π/7) \]

when you see the same two angles (pi/5 and pi/7) in 4 terms, you should get very suspicious, and see if the expression matches a sum or difference formula

the cos*cos is add to sin*sin
that means you have:

cos(a-b) = cos a cos b + sin a sin b

Answer 7

when I say match a and b line up the two expressions: yours and the formula
cos(a-b) = cos a cos b + sin a sin b
cos(π/5)cos(π/7)+sin(π/5)sin(π/7)
what is a and what is b?

Answer 8

this is not a trick question. Just say, if I match pi/5 with a and pi/7 with b, will I get the formula?

Answer 9

If they match (and they do) that means you can use this formula to simplify our expression.

Answer 10

not clear ?

Answer 11

i dont get it