Question

how does (cos pi/12 X cos pi/12) - (sin pi/12 x sin pi/12) = pi/6?

Answer 1

\[\cos(\frac{\pi}{12}) \cdot \cos(\frac{\pi}{12}) -\sin(\frac{\pi}{12}) \cdot \sin(\frac{\pi}{12})=\cos^2(\frac{\pi}{12})-\sin^2(\frac{\pi}{12})\]
Do you recall the following:
\[\cos^2(x)-\sin^2(x)=\cos(2x)\]

Answer 2

So here we clearly have
\[x=\frac{\pi}{12} => 2x=?\]

Answer 3

@shilohk ?

Answer 4

Do you understand? Do you know what 2x is if x=pi/12?

Answer 5

It doesn't equal pi/6. It equals cos(pi/6)

Answer 6

Freckles, yes, it would be 2pi/12 or pi/6... thank you!

Answer 7

:) Awesome shilohk! :)

Answer 8

So we have cos(pi/6)

Answer 9

So do you know how to evaluate that?

Answer 10

@Mertsj I was working with the inside first

Answer 11

The inside is pi/6 since x is pi/12 and 2x is 2pi/12=pi/6