Multiple choice

If 11x is an acute angle and $\displaystyle \tan 11x=\cot 7x$, then what is the value of x?

  1. $\displaystyle 5^{\circ}$
  2. $\displaystyle 6^{\circ}$
  3. $\displaystyle 7^{\circ}$
  4. $\displaystyle 8^{\circ}$
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A Correct answer
Explanation

tan(11x) = cot(7x) implies tan(11x) = tan(90 - 7x). Thus 11x = 90 - 7x, 18x = 90, x = 5.

AI explanation

Using the co-function identity cot(7x) = tan(90 degrees minus 7x), we can equate it to tan(11x). Since the angles are acute, we get 11x = 90 degrees minus 7x. Adding 7x to both sides gives 18x = 90 degrees. Dividing by 18 results in x = 5 degrees.

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