In a triangle ABC, the angle C is 90 °, tgA = √3 / 3. Find cosB. Will it not be equal to √3?

Since C = 90 °, triangle ABC is right-angled with legs √3 and 3. Using the Pythagorean theorem, we find the hypotenuse:

√ (√3) ^ 2 + 3 ^ 3) = √ (3 + 9) = 2√3.

Then, by the definition of the cosine of the angle, we get:

cos (B) = √3: 2√3 = 1/2.

The range of admissible values of the function y = cos (x) is the segment [-1; 1], √3 does not belong to this segment, therefore it cannot be the value of the sought cosine of angle B.

Answer: 1/2.