Question

If $\cos ec\theta =\frac{41}{40}$, then find the values of tan$\theta$ and cos$\theta$.

Answer 1

Given, $cosec\theta =\frac{41}{40}$

We know, $sin\theta =\frac{1}{cosec\theta }=\frac{40}{41}$

Since, ${\sin }^2\theta +{\cos }^2\theta =1$

$\therefore \cos \theta =\sqrt{1-{\sin }^2\theta }=\sqrt{1-{\left(\frac{40}{41}\right)}^2}=\frac{9}{41}$

Since, $\tan \theta =\frac{\sin \theta }{\cos \theta }=\frac{\frac{40}{41}}{\frac{9}{41}}=\frac{40}{9}$