Question

If cot A = tan A and 0 ≤ A ≤ 90°, the measure of angle A is ______.

Options

• 30°

• 60°

• 45°

• 90°

Answer 1

If cot A = tan A and 0 ≤ A ≤ 90°, the measure of angle A is 45°.

Explanation:

Given cot A = tan A. Since \[\cot A = \frac{1}{\tan A}\], this can be written as \[\frac{1}{\tan A} = \tan A \implies \tan^2 A = 1 \implies \tan A = 1\]. For 0 ≤ A ≤ 90°, the angle where tan A = 1 is A = 45°.