If sin (3x – 20°) = cos (3y + 20°), then find the value

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If sin (3x – 20°) = cos (3y + 20°), then find the value of (x + y).

1. 90°
2. 60°
3. 120°
4. 30°

Correct Option: D

sin (3x – 20°) = cos (3y + 20°)
⇒ sin (3x – 20°)
= sin {90° – (3y + 20°)}
[∵ sin (90° – θ) = cosθ]
⇒ 3x – 20° = 90° – 3y – 20° = 70° – 3y
⇒ 3x + 3y = 70° + 20° = 90°
⇒ 3 (x + y) = 90°

⇒ x + y =	90°	= 30°
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