How do you prove (tany+coty)/cscy=secy?

Sep 18, 2016

Explanation:

$\frac{\tan y + \cot y}{\csc} y$

= $\left(\sin \frac{y}{\cos} y + \cos \frac{y}{\sin} y\right) \times \frac{1}{\frac{1}{\sin} y}$

= $\frac{\sin y \times \sin y + \cos y \times \cos y}{\sin y \cos y} \times \sin y$

= $\frac{{\sin}^{2} y + {\cos}^{2} y}{\cancel{\sin} y \cos y} \times \cancel{\sin} y$

= $\frac{1}{\cos} y$

= $\sec y$