Question

If $cot\theta =\frac{9}{40}$, find the values of cosec $\theta$ and sec $\theta$.

Answer 1

We have , $cot\theta =\frac{9}{40}$

$\therefore cosec\theta =\sqrt{1+co{t}^2\theta }=\sqrt{1+{\left(\frac{9}{40}\right)}^2}=\sqrt{1+\frac{81}{1600}}=\sqrt{\frac{1681}{1600}}=\frac{41}{40}$

Now , $cot\theta =\frac{9}{40}\Rightarrow tan\theta =\frac{1}{cot\theta }=\frac{40}{9}$

$\therefore sec\theta =\sqrt{1+ta{n}^2\theta }\Rightarrow sec\theta =\sqrt{1+{\left(\frac{40}{9}\right)}^2}=\sqrt{\frac{1681}{81}}=\frac{41}{9}$