Multiple choice

If $\displaystyle \tan 2A= \cot (A-60^{\circ}),$ where 2A is an acute angle, then the value of A is

  1. $\displaystyle 30^{\circ}$
  2. $\displaystyle 60^{\circ}$
  3. $\displaystyle 50^{\circ}$
  4. $\displaystyle 24^{\circ}$
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C Correct answer
Explanation

tan(2A) = cot(A-60) = tan(90 - (A-60)) = tan(150 - A). 2A = 150 - A => 3A = 150 => A = 50 degrees.

AI explanation

Using the complementary angle identity, cot(A minus 60 degrees) equals tan(90 degrees minus(A minus 60 degrees)), which is tan(150 degrees minus A). Setting the angles equal gives 2A equals 150 degrees minus A. Solving this gives 3A equals 150 degrees, so A equals 50 degrees.

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