# Prove that the result depends on the variable

I have a formula:

$\dfrac{a_1\cdot\sin(-k\cdot x + \phi_1)+a_2\cdot\sin(k\cdot x + \phi_2)}{\ a_1\cdot\cos(-k\cdot x + \phi_1)+a_2\cdot\cos(k\cdot x + \phi_2)}$

I have to prove that, when $a_1 \neq a_2$ , the formula depends on x.

If $a_1 = a_2$ , it is clear that the result is $\tan\left(\dfrac{\phi_1+\phi_2}{2}\right)$, the result does not contains $x$.

Any suggestion?

Give two different values to $x$ and notice how the result is different. For example take $x = \phi_1 / k$, $x = \phi_2 / k$
• Thanks, but $x = -\dfrac{\phi_2}{k}$ is better for me, but anyway, the hint was helpful :) – User20141219 Jan 14 '15 at 9:40