Question

If cosecθ=√10 , find the value of all T– ratios of θ.​

Answer 1

Given :-

$\sf cosec \theta= \sqrt{10}$

To Find :-

All T- ratios of θ.

Solution :-

We know :-

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

$\therefore \sf sin \theta = \dfrac{1}{\sqrt{10}}$

We know :-

$\bf cos^2A = 1- sin^2A$

$\longrightarrow \sf cos^2A = 1- \left( \dfrac{1}{\sqrt{10}} \right)^2 \\\\\longrightarrow cos^2A = 1- \dfrac{1}{10} \\\\\longrightarrow cos^2 A = \dfrac{10-1}{10} \\\\\longrightarrow cos^2A = \dfrac{9}{10} \\\\\longrightarrow cosA = \sqrt{\dfrac{9}{10}} \\\\\longrightarrow cosA = \dfrac{3}{\sqrt{10}}$

We know :-

$\bf secA = \dfrac{1}{cosA}$

$\sf\therefore secA = \dfrac{\sqrt{10}}{3}$

We know :-

$\bf tanA = \dfrac{sinA}{cosA}$

$\therefore\sf tanA = \dfrac{1}{\sqrt{10}}\times \dfrac{\sqrt{10}}{3}$

           $= \sf \dfrac{1}{3}$

We know :-

$\bf cotA = \dfrac{1}{tanA}$

$\therefore\sf cotA = 3$