Question

If $\cot \theta =\frac{6}{8}$ and $\theta$ is acute, what is the value of $\text{cosec}\theta$?

• A. $\frac{6}{10}$
• B. $\frac{8}{10}$
• C. $\frac{10}{8}$
• D. $\frac{5}{10}$

Answer 1

Answer: (C)

$\frac{10}{8}$

First use the identity: $1+{\cot }^2\theta =\text{cosec}{}^2\theta$
and substitute the value of $\cot \theta =\frac{6}{8}$

Therefore, $1+{\left(\frac{6}{8}\right)}^2=\text{cosec}{}^2\theta$

$1+\sqrt{\frac{36}{64}}=\text{cosec}{}^2\theta$

$\text{cosec}\theta =\sqrt{\frac{100}{64}}$

Squaring on both the sides, we get
$\text{cosec}\theta =\frac{10}{8}$