Question

Express all trigonometric ratios in terms of secA

Answer 1

$sinA= \sqrt{sin^2A}$
$sinA= \sqrt{1-cos^2A}$
$sinA= \sqrt{1- \frac{1}{sec^2A} }$
$sinA= \sqrt{ \frac{sec^2A-1}{sec^2A} }$

======================================
$cosA= \frac{1}{secA}$

===============================================
$tanA= \sqrt{tan^2A}$
$tanA= \sqrt{sec^2A-1}$

=======================================
$cosecA= \frac{1}{sinA}$
$cosecA= \frac{1}{ \sqrt{sin^2A} }$
[tex]cosecA= \frac{1}{ \sqrt{1-cos^2A} } [/tex]
$cosecA= \frac{1}{ \sqrt{1- \frac{1}{sec^2} } }$
$cosecA= \frac{secA}{ \sqrt{sec^2A-1} }$

========================================

$cotA= \frac{1}{tanA}$
$cotA= \frac{1}{ \sqrt{tan^2A} }$
$cotA= \frac{1}{ \sqrt{sec^2A-1} }$