If x, y are acute angles, 0 < x + y < 90° and sin (2x

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If x, y are acute angles, 0 < x + y < 90° and sin (2x – 20°) = cos (2y + 20°), then the value of tan (x + y) is :

1. 1
  √3
2. √3
  2
3. √3
4. 1

Correct Option: D

sin (2x – 20°) = cos (2y + 20°)
⇒ sin (2x – 20°) = sin (90° – 2y – 20°)
⇒ 2x–20° = 70° – 2y
⇒ 2x + 2y = 70 +20 = 90°
⇒ x + y = 45°
∴ tan (x + y) = tan 45° = 1

	1
	√3

	√3
	2