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
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.
1 answer
1 answer