Help with proving a trigonometric identity

[kenshaw93]

Hi I've got this problem which has really been bothering me.

How are you supposed to prove that:
(Sin[A] Sin[2 A] + Sin[3 A] Sin[6 A])/(Sin[A] Cos[2 A] + Sin[3 A] Cos[6 A]) is identicle to tan[5A].

I am almost sure that I've got to use the factor formulae, but I've had no luck. Maybe someone can help me please :)
Thank you for your time!

 

[icystrike]

Hi I've got this problem which has really been bothering me.

How are you supposed to prove that:
(Sin[A] Sin[2 A] + Sin[3 A] Sin[6 A])/(Sin[A] Cos[2 A] + Sin[3 A] Cos[6 A]) is identicle to tan[5A].

I am almost sure that I've got to use the factor formulae, but I've had no luck. Maybe someone can help me please :)
Thank you for your time!

Try to "de-factor".
For instance, Sin(A)Sin(2A)=Sin(2A)Sin(A).
Recalling the identity that Cos S + Cos T = ?

 

[kenshaw93]

Ok i found out how to work it out. i first multiply by 2 throughout. then i used the factor formulae until i end up with the terms :

2sin5A sin4A / 2sin4Acos5A which is identicle to sin5A/cos5A which is identicle to tan5A...PROVED!

The satisfaction of proving an identity or equation is rather incredible!

 

[icystrike]

yea! Great sense of satisfaction. you are turning 17 this year?

 

[kenshaw93]

haha indeed i am, still young i guess, just scratching the surface of mathematics. The subject really gets you thinking