Multiple choice

If tan ⁑ 𝐴 + cot ⁑ 𝐴 = 2 , where 𝐴 A is an acute angle, then what is the value of tan ⁑2 𝐴 + cot ⁑2 𝐴 ?

  1. 2

  2. 6

  3. 8

  4. 15

  5. 67
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given tan A + cot A = 2. Square both sides: (tan A + cot A)^2 = 2^2 -> tan^2 A + cot^2 A + 2*tan A*cot A = 4. Since tan A * cot A = 1, we have tan^2 A + cot^2 A + 2 = 4, so tan^2 A + cot^2 A = 2.

AI explanation

Squaring both sides of the equation tan A + cot A = 2 gives tan^2 A + cot^2 A + 2 tan A cot A = 4. Using the trigonometric identity tan A cot A = 1, the equation simplifies to tan^2 A + cot^2 A + 2 = 4. Subtracting 2 from both sides leaves tan^2 A + cot^2 A = 2.

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