Question

tell me If sec theta = 13/12 then find cosec theta don't use Pythagoras theoram​

Answer 1

Answer:

The value of $cosec\ \theta$ is $\dfrac{13}{5}$ .

Step-by-step explanation:

We know that,

$\sec \theta =\dfrac{1}{\cos\theta}$

$cosec\ \theta =\dfrac{1}{\sin\theta}$

Also,

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

Given,

$\sec\theta = \dfrac{13}{12}$

Then,

$\cos \theta =\dfrac{12}{13}$

Using the identity, we have

$\sin^2\theta =1-\cos^2\theta= 1-(\frac{12}{13}) ^2=1-\dfrac{144}{169} =\dfrac{169-144}{169} =\dfrac{25}{169}$

Which implies

$\sin\theta = \dfrac{5}{13}$

Hence,

$cosec\ \theta=\dfrac{13}{5}$