Question

express cosec theta in terms of cos theta​

Answer 1

Step-by-step explanation:

cosec theta =

$\frac{1}{cos \: theta}$

Answer 2

Answer:

The expression of  $cosec\theta$ in terms of $cos\theta$  = $\sqrt{ \frac{1}{1-cos^2\theta}}$

Step-by-step explanation:

We know the trigonometrical identity

$sin^2\theta + cos^2\theta = 1$

Then,

$sin^2\theta = 1-cos^2\theta$ --------------(1)

Also, by another trigonometry identity, we have

$Sin\theta = \frac{1}{cosec\theta}$

So,

$Sin^2\theta = \frac{1}{cosec^2\theta}$

Substitute the value of $sin^2\theta$ in equation (1) we get

$\frac{1}{cosec^2\theta}$  =   $1- cos^2\theta$

By taking reciprocals on both sides we get,

$cosec^2\theta = \frac{1}{1-cos^2\theta}$

Hence the expression of  $cosec\theta$ in terms of $cos\theta$  = $\sqrt{ \frac{1}{1-cos^2\theta}}$