# Theorem

• Nov 13th 2012, 09:43 PM
chizmin10
Theorem
Use Theorem s(x+y)= s(x)c(y)+c(x)s(y) to show

cos(4x)= http://www3.wolframalpha.com/Calcula...s=6&w=155&h=18

Then apply this formula to find the value of cos(http://www3.wolframalpha.com/Calcula...&s=31&w=9&h=18/8)
• Nov 13th 2012, 09:58 PM
MarkFL
Re: Theorem
$\cos(4x)=\cos(2(2x))=1-2\sin^2(2x)=1-2(\sin(x+x))^2$

Now apply the angle-sum identity for sine as required.

Then use:

$x=\frac{\pi}{8}$ in the resulting formula. I would suggest letting $u=\cos^2(x)$ to get a quadratic in $u$. Take the appropriate root.