If 4θ is an acute angle, and cot 4θ = tan(θ - 5°), then what is the value of θ?
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Correct answer: A
Explanation
The correct answer is Option 1 i.e. 19°.
Given:
4θ is an acute angle,
And cot 4θ = tan(θ - 5°)
Formula used:
tan (90° - θ) = cot θ
Now, according to the question
cot 4θ = tan (θ - 5°)
⇒ tan (90° - 4θ) = tan (θ - 5°)
⇒ 90° - 4θ = θ - 5°
⇒ 90° + 5° = θ + 4θ
⇒ 95° = 5θ
⇒ θ = 19°
Thus, the value of θ is 19°.