Question

If $cosec2\theta =\sec \left(\theta -33°\right)$, where $2\theta$ is an acute angle, find the value of $\theta$.

Answer 1

Evaluating the given expression:

$cosec2\theta =\sec \left(\theta -33°\right)$

$\Rightarrow$$cosec2\theta =\cos ec\left(90°-(\theta -33°)\right)\left[\because sec\left(A\right)=\cos ec(90°-A)\right]$

$\Rightarrow$ $2\theta =(90°-(\theta -33°\left)\right)$

$\Rightarrow$ $2\theta =90°-\theta +33°$

$\Rightarrow$ $3\theta =123°$

$\Rightarrow$ $\theta =41°$

Hence, the value of the given expression is $41°$.