# Thread: Finding exact values using the sum and difference identity

1. ## Finding exact values using the sum and difference identity

How can I find the exact value of $cos\frac{\pi}{12}$ using the sum and difference identity?

I'm guessing I'd have to split the fraction up, into 2 parts, but I'm not sure on how to proceed.

Help appreciated.

2. ## Re: Finding exact values using the sum and difference identity

$\cos \left(\dfrac{\pi}{12}\right) = \cos \left(\dfrac{\pi}{4} - \dfrac{\pi}{6}\right)$

3. ## Re: Finding exact values using the sum and difference identity

Another way . . .

$\frac{\pi}{12} \;=\;\frac{4\pi}{12} - \frac{3\pi}{12} \;=\;\frac{\pi}{3} - \frac{\pi}{4}$

4. ## Re: Finding exact values using the sum and difference identity

you can also use the identity cos^2(x/2) = (1+cosx)/2

by taking (pie)/12 = [pie/6]/2

5. ## Re: Finding exact values using the sum and difference identity

Originally Posted by waqarhaider
you can also use the identity cos^2(x/2) = (1+cosx)/2

by taking (pie)/12 = [pie/6]/2
this is pi ...

this is pie ...

... hungry?