Question:
If sec 4A = cosec (A − 20°), where 4A is an acute angle, find the value of A.
Solution:
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°
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