If cot2(2η) = 3, where 2η is an acute angle, find the value of 5η.
75°
Given cot2(2η) = 3, so cot(2η) = ±√3. Since 2η is an acute angle, cot(2η) is positive, giving cot(2η) = √3.
From standard trigonometric values, cot 30° = √3.
Therefore 2η = 30°, which gives η = 15°.
Hence 5η = 5 × 15° = 75°.
Hence, the correct answer is 75°.
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