Question : If 4$\theta$ is an acute angle, and cot 4$\theta$ = tan($\theta$ – 5°), then what is the value of $\theta$?
Option 1: 19°
Option 2: 45°
Option 3: 21°
Option 4: 24°
Answer (1)
25th Jan, 2024
Correct Answer: 19°
Solution :
According to the question,
⇒ $\cot(4θ) = \tan(θ - 5°)$
⇒ $\cot(4θ) = \cot(90° - (θ - 5°))$
⇒ $4θ = 90° - (θ - 5°)$
⇒ $4θ +θ - 5° = 90°$
⇒ $5θ = 95° $
⇒ $θ =19°$
Hence, the correct answer is 19°.
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