Zināms, ka \(\frac{\cos 3x}{\cos x}=\frac{1}{2015}\). Aprēķināt \(\frac{\sin 3x}{\sin x}\) vērtību!
Aplūkosim starpību
\[\frac{\sin 3x}{\sin x}-\frac{\cos 3x}{\cos x}=\frac{\sin 3x \cos x-\cos 3x \sin x}{\sin x \cdot \cos x}=\frac{\sin (3x-x)}{\sin x \cdot \cos x}=\frac{\sin 2x}{\sin x \cdot \cos x}=\frac{2 \sin x \cdot \cos x}{\sin x \cdot \cos x}=2\]
Tātad \(\frac{\sin 3x}{\sin x}=2+\frac{1}{2015}=\frac{4031}{2015}\).