Trigonometric ratios of angle A in terms of cot A

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

Value of sin A in terms of cot A

From Trigonometric Identity

$cosec^2 A = 1 + cot^2 A$
or
$\frac {1}{\sin^2 A} = 1 + cot^2 A$
$\sin A = \frac {1}{\sqrt {1 + cot^2 A}}$

Value of cos A in terms of cot A

$\cos ^2 A = 1 – \sin^2 A= 1 – \frac {1}{1 + cot^2 A}= \frac {cot^2 A}{1 + cot^2 A}$
Hence

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

Value of tan A in terms of cot A

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

Value of cosec A in terms of cot A

Now Value of cosec is given by

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

Value of sec A in terms of cot A

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

In short