Question 5
If $s e c 4 A = c o s e c (A - 20^{\circ})$ , where 4A is an acute angle, find the value of A.

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Solution

According to the question,
$s e c 4 A = c o s e c (A - 20^{\circ})$
Since $c o s e c (90 - θ) = s e c θ$
$\Rightarrow c o s e c (90^{\circ} - 4 A) = c o s e c (A - 20^{\circ})$

Equating angles,
$90^{\circ} - 4 A = A - 20^{\circ}$
$\Rightarrow 110^{\circ} = 5 A$
$\Rightarrow A = 22^{\circ}, (a n a c u t e a n g l e) .$

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