Question

sec θ when expressed in term of cot θ, is equal to ______.

पर्याय

• ${\displaystyle \frac{1+{\cot }^2\theta }{\cot \theta }}$

• ${\displaystyle \sqrt{1+{\cot }^2\theta }}$

• ${\displaystyle \frac{\sqrt{1+{\cot }^2\theta }}{\cot \theta }}$

• ${\displaystyle \frac{\sqrt{1-{\cot }^2\theta }}{\cot \theta }}$

Answer 1

sec θ when expressed in term of cot θ, is equal to ${\displaystyle \underline{\frac{\sqrt{1+{\cot }^2\theta }}{\cot \theta }}}$.

Explanation:

As we know that,

sec² θ = 1 + tan² θ

and cot θ = ${\displaystyle \frac{1}{\tan \theta }}$

${\displaystyle \Rightarrow }$ tan θ = ${\displaystyle \frac{1}{\cot \theta }}$

∴ sec² θ = ${\displaystyle 1+{\left(\frac{1}{\cot \theta }\right)}^2}$

= ${\displaystyle 1+\frac{1}{{\cot }^2\theta }}$

${\displaystyle \Rightarrow }$ sec² θ = ${\displaystyle \frac{{\cot }^2\theta +1}{{\cot }^2\theta }}$

${\displaystyle \Rightarrow }$ sec θ = ${\displaystyle \frac{\sqrt{1+{\cot }^2\theta }}{\cot \theta }}$