## VeroZarate 2 years ago Find an exact value: cos(pi/12)

1. mathmate

let y=cos(pi/12), then apply the double angle formula: cos^2(x)-sin^2(x)=cos(2x) or, substituting sin^2(x)+cos^2(x)=1, 2cos^2(x)-1=cos(2x) cos^2(x)=(1+cos(2x))/2 let x=pi/12 then cos^2(pi/12)=(1+cos(pi/6))/2 Since cos(pi/6) is known to be sqrt(3)/2, cos(pi/12)=sqrt((1+sqrt(3)/2)/2)

2. VeroZarate

im sorry but thats not one of my options

3. VeroZarate

i somehow have to use the sum and difference formulas

4. mathmate

Are they in numerical values?

5. VeroZarate

yes they all have sqrt6 and sqrt2 over 4 but with different signs +/-

6. mathmate

cos^2(x)-sin^2(x)=cos(2x) is from the double angle formula.

7. VeroZarate

how would you split pi/12? i think thats what i need to do?

8. mathmate

You will need to evaluate each option to see if it evaluates to: sqrt((1+sqrt(3)/2)/2) which can be written as sqrt((2+sqrt(3)/4) or sqrt(2+sqrt(3))/2 Why don't you post the options if you're not sure?

9. VeroZarate

ok i think i got it thanks!!

10. mathmate

yw! :)