Trigonometric ratios of angle A in terms of tan A

In this post ,we will see how we can write all the Trigonometric ratios of angle A in the terms of sin A. Here we would be focusing on acute angle A only

Value of cos A in terms of tan A

From Trigonometric Identity

$\sec ^2 A =1 + \tan ^2 A$
or
$\frac {1}{\cos ^2 A}= 1 + \tan ^2 A$
$\cos A = \frac {1}{\sqrt { 1 + \tan ^2 A}$

Value of sin A in terms of tan A

$\tan A = \frac {\sin A}{\cos A}$
$\sin A = \tan A \cos A$
$\sin A = \frac {\tan A}{\sqrt { 1 + \tan ^2 A}}$

Value of cosec A in terms of tan A

Now Value of cosec is given by

$\csc A = \frac {1}{\sin A} = \frac {\sqrt { 1 + \tan ^2 A}}{\tan A}$

Value of sec A in terms of tan A

$sec A = \frac {1}{cos A} = \sqrt { 1 + \tan ^2 A}$

Value of cot A in terms of tan A

$\cot A = \frac {1}{\tan A} $

In Short