Question

If $\sec 3\beta =cosec\left(\beta -22°\right)$ and $3\beta$ is an acute angle, find the value of $\beta$.

Answer 1

Evaluating the given expression:

$\sec 3\beta =cosec\left(\beta -22°\right)$

$\Rightarrow \mathrm{cosec}(90°-3\beta )=cosec\left(\beta -22°\right)\left[\because \cos ec(90°-A)=secA\right]$

$\Rightarrow$ $90°-3\beta =\beta -22°$

$\Rightarrow$ $4\beta =90°+22°$

$\Rightarrow$ $4\beta =112°$

$\Rightarrow$ $\beta =28°$

Hence, the value of the given expression is $28°$.