Expand expression sen(2pi/3)-cos (2pi/3) to get 2sen(pi/3)cos(pi/3)-1+2sen^2 (pi/3)

[schools and math]

Hello,
I need some help, please
I need to expand the following expression

sen (2pi/3) - cos (2pi/3)

I checked the solutions, and it is supposed to equal the next expression:

2 sen (pi/3) cos (pi/3) -1 +2 sen^2 (pi/3)

I have already tried to decompose 2pi/3 in pi - pi/3. Then I got:

sen (pi- pi/3) - cos (pi - pi/3)

Then i applied the formula:
sen pi cos pi/3 - sen pi/3 cos pi - (cos pi cos pi/3 + sen pi cos pi/3)

However I am a bit stuck - I am not even sure if I am going the right way - doesn't seem like it.

Thank you so very much for all you help

 

[tkhunny]

Try these: http://www.purplemath.com/modules/idents.htm

About half-way down, find "Double-Angle Identities".

 

[schools and math]

Got it!
2* pi/3! Thank you! I was going in another direction and it was actually pretty easy