Simplifying a ratio of sines with angle perturbations

[hermano]

Hi,

I'm trying to simplify the following equation, but I'm not sure it can be! Can anybody help me please?

$$\frac{sin(\alpha + \delta \alpha)} {sin(\beta + \delta \beta - \alpha - \delta \alpha)} - \frac{sin(\alpha)} {sin(\beta - \alpha)}$$

 

[berkeman]

Hi,

I'm trying to simplify the following equation, but I'm not sure it can be! Can anybody help me please?

$$\frac{sin(\alpha + \delta \alpha)} {sin(\beta + \delta \beta - \alpha - \delta \alpha)} - \frac{sin(\alpha)} {sin(\beta - \alpha)}$$

That's not an equation (no equal sign), it is an expression. What is the full equation?

What is the context of the question? Is it for schoolwork, or for a physical problem?

 

[hermano]

That's not an equation (no equal sign), it is an expression. What is the full equation?

What is the context of the question? Is it for schoolwork, or for a physical problem?

Oke, the full equation is
$$\epsilon = \frac{sin(\alpha + \delta \alpha)} {sin(\beta + \delta \beta - \alpha - \delta \alpha)} - \frac{sin(\alpha)} {sin(\beta - \alpha)}$$

It is for an error analyses of a physical problem!

Thanks

 

[I like Serena]

Welcome to PF, hermano!

Let's define $f(x) = {\sin(\alpha x) \over sin(\gamma x)}$.
Do you know what the definition of f'(1) is?