# Proving this trigonometric identity

1. May 26, 2012

### hms.tech

1. The problem statement, all variables and given/known data
Show that :

1 + cos(2∏/5)= 2 cos(∏/5)

2. Relevant equations

cos(2x) = cos^2(x)-sin^2(x)
cos^2(x)+sin^2(x) = 1

3. The attempt at a solution

I have tried using the two formulas above but i couldn't show the required result.

2. May 26, 2012

### ehild

It is not true. ∏/5=36° , 1+cos(72°)≠2cos(36°)

ehild

3. May 26, 2012

### sacscale

Looks like the identity should have been:

1 + cos(2∏/5) = 2 cos^2(∏/5)

4. May 26, 2012

### SammyS

Staff Emeritus
Hello sacscale. Welcome to PF !

I believe that you are correct !

5. Jun 16, 2012

### hms.tech

Yes but the issue remains, how do we prove it ?

6. Jun 16, 2012

### Staff: Mentor

Assuming you are trying to prove 1 + cos(2$\pi$/5) = cos2($\pi$/5) rather than what you originally posted, rewrite the left side using the double angle identity.

7. Jun 25, 2012

### hms.tech

alright, got it
thnx