x, y be two acute angles, x + y < 90° and sin(2x - 20°) = cos(2y + 20°), the value of tan(x + y) is?

A. $$\sqrt 3 $$

B. $$\frac{1}{{\sqrt 3 }}$$

C. 1

D. $${\text{2}} + \sqrt 2 $$

Answer: Option C

Solution(By Examveda Team)

sin(2x - 20) = cos(2y + 20)
⇒ sin(2x - 20) = sin(90 - (2y + 20))
i.e. 2x - 20 = 90 - 2y - 20
⇒ 2x + 2y = 90
⇒ x + y = 45°
∴ tan(x + y) = tan 45° = 1