1. Diketahui nilai yang harus dicari adalah $$\tan(-340^\circ) \cdot \sin 200^\circ \cdot \cos 20^\circ$$. 2. Rumus yang digunakan: - Identitas sudut negatif: $$\tan(-\theta) = -\tan \theta$$ - Hubungan sudut: $$\sin(180^\circ + \alpha) = -\sin \alpha$$ dan $$\cos(180^\circ + \alpha) = -\cos \alpha$$ 3. Hitung $$\tan(-340^\circ)$$: $$\tan(-340^\circ) = -\tan 340^\circ$$ Karena $$340^\circ = 360^\circ - 20^\circ$$, maka $$\tan 340^\circ = -\tan 20^\circ$$ Jadi, $$\tan(-340^\circ) = -(-\tan 20^\circ) = \tan 20^\circ$$ 4. Hitung nilai $$\sin 200^\circ$$: $$\sin 200^\circ = \sin(180^\circ + 20^\circ) = -\sin 20^\circ$$ 5. Nilai $$\cos 20^\circ$$ tetap. 6. Substitusi ke dalam ekspresi: $$\tan(-340^\circ) \cdot \sin 200^\circ \cdot \cos 20^\circ = \tan 20^\circ \cdot (-\sin 20^\circ) \cdot \cos 20^\circ = -\tan 20^\circ \sin 20^\circ \cos 20^\circ$$ 7. Gunakan identitas $$\tan \theta = \frac{\sin \theta}{\cos \theta}$$: $$-\tan 20^\circ \sin 20^\circ \cos 20^\circ = -\frac{\sin 20^\circ}{\cos 20^\circ} \cdot \sin 20^\circ \cdot \cos 20^\circ = -\sin^2 20^\circ$$ 8. Jadi, nilai akhirnya adalah: $$\boxed{-\sin^2 20^\circ}$$