Theorem

**chizmin10** · November 13th 2012, 08:43 PM

Use Theorem s(x+y)= s(x)c(y)+c(x)s(y) to show

cos(4x)=

Then apply this formula to find the value of cos(

/8)

**MarkFL** · November 13th 2012, 08:58 PM

$\cos(4x)=\cos(2(2x))=1-2\sin^2(2x)=1-2(\sin(x+x))^2$

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.

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