If tan 3θ = cot(θ - 22°), where 3θ is an acute angle, find the value of θ.
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 28°.
tan 3θ = cot(θ - 22°), where 3θ is acute (0° < 3θ < 90°)
cot(θ - 22°) = tan[90° - (θ - 22°)] = tan(112° - θ)
So, tan 3θ = tan(112° - θ)
⇒ 3θ = 112° - θ
⇒ 4θ = 112°
⇒ θ = 112°/4 = 28°