Multiple choice

The numerical value of $\tan {20^{\circ}}\tan {80^{\circ}} \cot {50^{\circ}}$ is equal to

  1. $\sqrt {3}$
  2. $\dfrac {1}{\sqrt {3}}$
  3. $2\sqrt {3}$
  4. $\dfrac {1}{2\sqrt {3}}$
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A Correct answer
Explanation

Use the identity tan(20)tan(80)cot(50) = tan(20)tan(80)tan(40). Using the identity tan(theta)tan(60-theta)tan(60+theta) = tan(3*theta), we set theta=20. Then tan(20)tan(40)tan(80) = tan(60) = sqrt(3).

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