SOLUTION: 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 t

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.
Found 4 solutions by solver91311, tokeins, ikleyn, MathTherapy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Show one of the many ways you have tried to solve this and then I'll help you.

John

My calculator said it, I believe it, that settles it

Answer by tokeins(1)   (Show Source): You can put this solution on YOUR website!
I tried the formula using Cos(A+B)=CosA*CosB+SinA*SinB..plugged everything in and then added the two cos together to get Cos 14pi/18 then simplified to Cos 7pi/9 this is where am currently stuck at.
Edit: Oh I see my mistake, thanks... I added the 13pi and pi together instead of subtracting them.
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
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
-----------------------------------------------------------

It is simple. The key is to apply the subtraction formula for cosines:

Cos() * Cos() + Sin() * Sin() =

    ( use the facts that Cos() = Cos(), Sin() = -Sin() )

= Cos() * Cos() - Sin() * Sin() =
    (now apply the subtraction formula for cosines, see the lesson
      Addition and subtraction formulas in this site)

= cos ( - ) = cos() = cos() = .

That's all.

Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
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.

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:
=
Reducing , we get:
is in the 2^nd quadrant, its reference angle is: and it's negative (< 0), so = =
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