Question

If $\sec 4A=\csc (A$ - ${20}^{\circ }$), where $4A$ is an acute angle, find the value of A.

Answer 1

Given,

$4A$ is acute and $\sec 4A=\csc (A-{20}^{\circ })$

We have, $\sec \theta =\csc ({90}^{\circ }-\theta )$

$\sec 4A=\csc ({90}^{\circ }-4A)$

$\therefore \csc ({90}^{\circ }-4A)=\csc (A-{20}^{\circ })$

$({90}^{\circ }-4A)=(A-{20}^{\circ })$

${110}^{\circ }=5A$

$5A={110}^{\circ }$

$A=\frac{{110}^{\circ }}{5}$

$\theta ={22}^{\circ }$