Question.
If sec 4 A = cosec (A – 20°), where 4 A is an acute angle, find the value of A.
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°)
$\Rightarrow \operatorname{cosec}\left(90^{\circ}-4 \mathrm{~A}\right)=\operatorname{cosec}\left(\mathrm{A}-20^{\circ}\right)$
$\left\{\because \operatorname{cosec}\left(90^{\circ}-\theta\right)=\sec \theta\right\}$
$\Rightarrow 90^{\circ}-4 \mathrm{~A}=\mathrm{A}-20^{\circ}$
$\Rightarrow 5 \mathrm{~A}=110^{\circ} \Rightarrow \mathrm{A}=22^{\circ}$
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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