Question

If $\sec 2\beta =cosec\left(\beta -24°\right)$ and $2\beta$ is an acute angle, find the value of $\beta .$

Answer 1

Finding the value of $\beta :$

Given that,
$\sec 2\beta =cosec\left(\beta -24°\right)$
$\sec 2\beta =\sec \left(90°-\beta +24°\right)$
$2\beta =114°-\beta$
$\beta =38°$

Hence, the value of $\beta =38°$