If sec 4 A = cosec (A – 20°),
Question.

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

Solution:

sec 4 A = cosec (A – 20°)

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

$\left\{\because \operatorname{cosec}\left(90^{\circ}-\theta\right)=\sec \theta\right\}$

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

$\Rightarrow 5 \mathrm{~A}=110^{\circ} \Rightarrow \mathrm{A}=22^{\circ}$
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