x and y be two acute angles, x + y < 90° and sin(2x - 20°) = cos(2y + 20°), the value of tan(x + y) is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 1.
sin(2x - 20°) = cos(2y + 20°)
⇒ sin(2x - 20°) = sin[90° - (2x - 20°)]
⇒ 2x - 20 = 90° - (2y + 20°)
⇒ 2x + 2y = 90°
⇒ x + y = 45°
Hence,
tan(x + y) = tan 45° = 1