Question

Please Help
sec x/tan x =csc x

Answer 1

Rewrite everything in terms of sine and cosine
\[\large \frac{sec(x)}{tan(x)} = csc(x)\]
Since you know \(\large sec(x) = \frac{1}{cos(x)}\) and \(\large tan(x) =\frac{sin(x)}{cos(x)}\) you can write this as:
\[\large \frac{\frac{1}{cos(x)}}{\frac{sin(x)}{cos(x)}} = \frac{1}{sin(x)}\]

You'll notice
\[\large \frac{\frac{1}{\cancel{cos(x)}}}{\frac{sin(x)}{\cancel{cos(x)}}} = \frac{1}{sin(x)}\]

Leaving you with
\[\large \frac{1}{sin(x)} = \frac{1}{sin(x)} \color \red{\checkmark}\]

Answer 2

Thank you for explaining it