Question:
If $\sec 4 A=\operatorname{cosec}\left(A-20^{\circ}\right)$, where $4 A$ is an acute angles, find the value of $A$.
Solution:
Given: $\sec 4 A=\operatorname{cosec}\left(A-20^{\circ}\right)$ and $4 A$ is an acute angle
We have to find $\theta$
Now
$\sec 4 A=\operatorname{cosec}\left(A-20^{\circ}\right)$
$\sec 4 A=\sec \left\{90^{\circ}-\left(A-20^{\circ}\right)\right\}$
$\sec 4 A=\sec \left(90^{\circ}-A+20^{\circ}\right)$
$\sec 4 A=\sec \left(110^{\circ}-A\right)$
$5 A=110^{\circ}$
$A=22^{\circ}$
Hence the value of $A$ is $22^{\circ}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.