Trigonometric riddle

[shahar]

The riddle is:
You need to achieve the expression sin(alpha + beta) by those four expressions only:
sin(alpha), sin(beta), cos(alpha) and cos(beta).
Any solution will help.
Or Hints to solution if you want.

 

[topsquark]

Do you know the trig addition formulas?
[math]sin( \alpha \pm \beta ) = sin( \alpha ) ~ cos( \beta ) \pm sin( \beta ) ~ cos( \alpha )[/math]
[math] cos( \alpha \pm \beta ) = cos( \alpha ) ~ cos( \beta ) \mp sin( \alpha ) ~ sin( \beta )[/math]
[math]tan( \alpha \pm \beta ) = \dfrac{tan( \alpha ) \pm tan( \beta )}{ 1 \mp tan( \alpha ) ~ tan( \beta )}[/math]
-Dan

 

[shahar]

nice. thanks. these identities, right?

 

[topsquark]

nice. thanks. these identities, right?

Yep. Good for all angles.

-Dan