Multiple choice

The value of $\displaystyle\frac{\cot{40^\circ}}{\tan{50^\circ}}-\frac{1}{2}\left(\frac{\cos{35^\circ}}{\sin{55^\circ}}\right)$ is ____________.

  1. $\displaystyle\frac{1}{\sqrt{2}}$

  2. 0

  3. 1
  4. $\displaystyle\frac{1}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

cot(40) = tan(50), so the first term is 1. cos(35) = sin(55), so the second term is 1/2 * (1) = 1/2. 1 - 1/2 = 1/2.

AI explanation

Using the complementary angle identities, cot 40 degrees equals tan 50 degrees and cos 35 degrees equals sin 55 degrees. The first term simplifies to tan 50 degrees divided by tan 50 degrees, which is 1. The second term simplifies to one half multiplied by sin 55 degrees divided by sin 55 degrees, which is one half, leaving 1 minus 1/2 equals 1/2.

Keep practicing — related questions