Question

Prove tany + Coty = 2Cosec2y
Answer properly u will be brainliest

Answer 1

Step-by-step explanation:

First

$\tan y+\cot y=\dfrac{\sin y}{\cos y}+\dfrac{\cos y}{\sin y}=\dfrac{\sin^2y+\cos^2y}{\sin y\cos y} =\dfrac{1}{\sin y\cos y}$

and as   $\sin(2y)=2\sin y\cos y$

we get

$\tan y+\cot y=\dfrac{1}{\sin y\cos y}= \dfrac{2}{2\sin y\cos y}=\dfrac{2}{\sin 2y}=2\csc2y$