If $sec 2 A = cosec (A - 42),$ where $2 A$ is the measure of an acute angle , Find the value of A .

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Solution

$2 A$ is measure of acture angle $2 A ∠ 90^{\circ}$
$\Rightarrow A ∠ 45^{\circ}$
$s e c 2 A = c o s e c (A - 42)$
$\frac{1}{c o s (2 A)} = \frac{1}{s i n (A - 42)}$
$s i n (A - 42) = c o s (2 A) = s i n (90 - 2 A)$
$(∵ 2 A ∠ 90^{\circ})$
$\Rightarrow s i n (A - 42) = s i n (90 - 2 A)$
$\Rightarrow A - 42 = 90 - 2 A$
$3 A = 132$
$A = \frac{132}{3} = 44^{\circ}$

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