Multiple choice

If 4θ is an acute angle, and cot 4θ = tan(θ - 5°), then what is the value of θ?

  1. 19°

  2. 45°

  3. 21°

  4. 24°
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A Correct answer
Explanation

Given cot(4theta) = tan(theta - 5). Since cot(x) = tan(90 - x), we have tan(90 - 4theta) = tan(theta - 5). Thus, 90 - 4theta = theta - 5. Solving for theta: 5theta = 95, so theta = 19 degrees.

AI explanation

Using the co-function identity, cot(4θ) equals tan(90 degrees minus 4θ). Setting this equal to tan(θ minus 5 degrees) gives the equation 90 minus 4θ equals θ minus 5. Solving for θ yields 5θ equals 95, so θ equals 19 degrees.

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