Question

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

Answer 1

$\text{cosec}(90°-x)=\sec x$

According to question,

$\therefore \sec \left(4A\right)=\text{cosec}(A-20)\text{cosec}(90°-4A)=\text{cosec}(A-20)$

$\therefore 90°-4A=A-20°$

$110°=5A$

$\therefore A=\frac{110°}{5}=22°$

$\angle A=22°$