bentuk sederhana dari cos 3x-sin 6x-cos 9x / sin 9x-cos 6x- sin 3x adalah...

Trigonometry.

cos A - cos B = -2 sin [(A + B) / 2] sin [(A - B) / 2]
sin A - sin B = 2 cos [(A + B) / 2] sin [(A - B) / 2]

[tex]\displaystyle \frac{\cos 3x-\sin 6x-\cos 9x}{\sin 9x-\cos 6x-\sin 3x}\\ =\frac{\left [ -2\sin \left ( \frac{3x+9x}{2} \right )\sin \left ( \frac{3x-9x}{2} \right ) \right ]-\sin 6x}{\left [2\cos \left ( \frac{9x+3x}{2} \right )\sin \left ( \frac{9x-3x}{2} \right ) \right ]-\cos 6x}\\ =\frac{[-2\sin 6x \sin (-3x)]-\sin 6x}{(2\cos 6x \sin 3x)-\cos 6x}\\ =\frac{\sin 6x(2\sin 3x-1)}{\cos 6x(2\sin 3x-1)}\\ =\tan 6x[/tex]