Question : If $\sec 3\mathrm{A}=\operatorname{cosec}\left(\mathrm{A}-72^{\circ}\right)$, then what is the value of A ?
Option 1: 34.5°
Option 2: 30°
Option 3: 40.5°
Option 4: 25°
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Correct Answer: 40.5°
Solution :
$\sec 3A = \operatorname{cosec} (A - 72°)$
⇒ $\sec 3A = \sec [90° - (A - 72°)]$
⇒ $\sec 3A = \sec (162° - A)$
⇒ $3A = 162° - A$
⇒ $4A = 162°$
⇒ $A = 40.5°$
Hence, the correct answer is 40.5°.
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