Proving this trigonometric identity

[hms.tech]

Homework Statement

Show that :

1 + cos(2∏/5)= 2 cos(∏/5)

Homework Equations

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

The Attempt at a Solution

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

 

[ehild]

Homework Statement

Show that :

1 + cos(2∏/5)= 2 cos(∏/5)

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

ehild

 

[sacscale]

Looks like the identity should have been:

1 + cos(2∏/5) = 2 cos^2(∏/5)

 

[SammyS]

Looks like the identity should have been:

1 + cos(2∏/5) = 2 cos^2(∏/5)

Hello sacscale. Welcome to PF !


I believe that you are correct !

 

[hms.tech]

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

 

[Mark44]

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

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.

 

[hms.tech]

alright, got it
thnx