Bentuk sederhana dari cos 3x - sin 6x - cos 9x / sin 9x - cos 6x - sin 3x

Trigonometri.

[tex]\displaystyle \boxed {\cos A-\cos B=-2\sin \left ( \frac{A+B}{2} \right )\sin\left ( \frac{A-B}{2} \right )}\\ \boxed{\sin A-\sin B=2\cos \left ( \frac{A+B}{2} \right )\sin \left ( \frac{A-B}{2} \right )}[/tex]

[tex]\displaystyle \frac{\cos 3x-\sin 6x-\cos 9x}{\sin 9x-\cos 6x-\sin 3x}\\ =\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]