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

19^{\circ}

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20^{\circ}

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21^{\circ}

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22^{\circ}

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Solution

The correct option is D $22^{\circ}$
$S e c 4 A = c o s e c (A - 20^{\circ})$
$\Rightarrow c o s e c (90^{\circ} - 4 A) = c o s e c (A - 20^{\circ})$
$\Rightarrow 90^{\circ} - 4 A = A - 20^{\circ}$
$\Rightarrow 110^{\circ} = 5 A$
$\Rightarrow A = 22^{\circ}$

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