Question

Cos/1-tg +sen/1-cotang=sen+ cos
Por favor ayudita hay que comprobar la identidad.

Answer 1

$E=\dfrac{\cos \alpha}{1-\tan\alpha}+\dfrac{\sin \alpha}{1-\cot\alpha}\\ \\ \\ E=\dfrac{\cos \alpha}{1-\dfrac{\sin\alpha}{\cos\alpha}}+\dfrac{\sin \alpha}{1-\dfrac{\cos\alpha}{\sin\alpha}}\\ \\ \\ E=\dfrac{\cos^2\alpha}{\cos\alpha-\sin\alpha}+\dfrac{\sin^2\alpha}{\sin\alpha-\cos\alpha}\\ \\ \\ E=\dfrac{\cos^2\alpha}{\cos\alpha-\sin\alpha}-\dfrac{\sin^2\alpha}{\cos\alpha-\sin\alpha}$


$E=\dfrac{\cos^2\alpha-\sin^2\alpha}{\cos\alpha-\sin\alpha}\\ \\ \\ E=\dfrac{(\cos\alpha-\sin\alpha)(\cos\alpha+\sin\alpha)}{\cos\alpha-\sin\alpha}\\ \\ \\ \boxed{\boxed{E=\cos\alpha+\sin\alpha}}$