Question : If $α$ is an acute angle, $\tan (4α − 50°) = \cot (50° − α)$, then find the value of $α$ (in degrees).
Option 1: 60
Option 2: 45
Option 3: 30
Option 4: 90
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Correct Answer: 30
Solution :
$\tan (4α − 50°)$ = $\cot (50° − α)$ = $\tan(90°–(50° − α))$
⇒ $\tan (4α − 50°)$ = $\tan(90°–(50° − α))$
⇒ $(4α − 50°) = 90°–(50° − α)$
⇒ $4α − 50° = 40°+α$
⇒ $3α = 90°$
⇒ $α = 30°$
Hence, the correct answer is 30.
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