Question 1005071
Using Trigonometry Identities. Simplify the expression into one trigonometric function then evaluate if possible. 

Cos 13pi/18 * Cos pi/18 + Sin 13pi/18 * Sin pi/18

I tried this problem many different ways but I'm not sure exactly how to do it.
<pre>You need to use the "Difference of 2 angles" Identity, not the "Sum of 2 angles" identity.
Difference of 2 angles identity: cos(A - B) = cos A cos B + sin A sin B. Compare this to: {{{cos (13pi/18) * cos (pi/18) + sin (13pi/18) * sin (pi/18)}}}
{{{cos(A - B) = cos (13pi/18 - pi/18)}}} = {{{cos (12pi/18)}}}
Reducing {{{12pi/18}}}, we get: {{{2pi/3)}}}
{{{cos (2pi/3)}}} is in the 2<sup>nd</sup> quadrant, its reference angle is: {{{pi/3}}} and it's negative (< 0), so {{{cos (2pi/3)}}} = {{{- cos (pi/3)}}} = {{{highlight_green(- 1/2)}}}