If sec 4A = cosec (A − 20°),

Given that:

$\sec 4 A=\operatorname{cosec}\left(A-20^{\circ}\right)$, then we have to find the value of $A$

Since it is given that the angle 4A is acute angle, therefore we can apply the identity 

Therefore the given equation can be written as

$\operatorname{cosec}\left(90^{\circ}-4 A\right)=\operatorname{cosec}\left(A-20^{\circ}\right)$

$\Rightarrow \quad 90^{\circ}-4 A=A-20^{\circ}$

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

$\Rightarrow \quad A=22^{\circ}$

Hence the value of A is 22°