Question

Simplifique a expressão:

sen50 + sen30 / cos(-30) + cos10

Answer 1

Apliquemos las siguientes identidades

             $\sin A +\sin B = 2\sin\left(\dfrac{A+B}{2}\right)\cos \left(\dfrac{A-B}{2}\right)\\ \\ \\ \cos A + \cos B = 2\cos \left(\dfrac{A+B}{2}\right)\cos \left(\dfrac{A-B}{2}\right)$

Entonces

             $\dfrac{\sin 50+\sin 30}{\cos (-30)+\cos 10}=\dfrac{\sin 50+\sin 30}{\cos 30+\cos 10}\\ \\ \\ \dfrac{\sin 50+\sin 30}{\cos (-30)+\cos 10}=\dfrac{2\sin 40\cos 10}{2\cos 20\cos 10}\\ \\ \\ \dfrac{\sin 50+\sin 30}{\cos (-30)+\cos 10}=\dfrac{\sin 40}{\cos 20}\\ \\ \\ \dfrac{\sin 50+\sin 30}{\cos (-30)+\cos 10}=\dfrac{2\sin 20\cos 20}{\cos 20}\\ \\ \\ \boxed{\dfrac{\sin 50+\sin 30}{\cos (-30)+\cos 10}=2\sin 20}$