Question
If $\sec2\text{A}=\text{cosec(A}-42^\circ),$ where 2A is an acute angles, find the value of A.
✓
Answer
We know that $(\sec(90-\theta))=\text{cosec }\theta$
$\sec2\text{A}=\sec(90-(\text{A}-42))$
$ \sec2\text{A}=\sec(90-\text{A}+42)$
$\sec2\text{A}=\sec(132-\text{A})$
Now equating both the angles we get
$2\text{A}=132-\text{A}$
$3\text{A}=132$
$\text{A}=44$
$\sec2\text{A}=\sec(90-(\text{A}-42))$
$ \sec2\text{A}=\sec(90-\text{A}+42)$
$\sec2\text{A}=\sec(132-\text{A})$
Now equating both the angles we get
$2\text{A}=132-\text{A}$
$3\text{A}=132$
$\text{A}=44$
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