Posted by **Anonymous** on Friday, April 27, 2012 at 11:59pm.

Question: Trying to find cos π/12, if cos π/6 = square root 3 over 2, how to find cos π/12 using DOUBLE angle formula?

This is what I got so far..

cos 2(π/6) = cos (π/6 + π/6)

= (cos π/6)(cos π/6) - (sin π/6)(sin π/6)

= cos^2 π/6 - sin^2 π/6

Is that right? Please and thank you.

- Trig Help! -
**Reiny**, Saturday, April 28, 2012 at 12:13am
you got it backwards

π/12 = (1/2) of π/6

using cos 2A = cos^2 A - sin^2 A = 2cos^2 A - 1

so cos π/6 = 2 cos^2 π/12 - 1

√3/2 + 1 = 2cos^2 π/12

cos^2 π/12 = √3/4 + 1/2 = (√3 + 2)/4

**cos π/12 = √(√3+2) /2**

check:

by calculator, cos π/12 = .96592...

√(√3+2)/2 = .96592...

My answer is correct.

Of course the answer I gave is not unique

we could have done it this way

cos π/12 = cos 15°

= cos(45-30)°

= cos45cos30 + sin45sin30

= (√2/2)(√3/2) + (√2/2)(1/2) = **(√6 + √2)/4**

which when evaluated is also .96592...

but it asked for a solution using the double angle formula

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