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x, y be two acute angles, x + y < 90° and sin(2x - 20°) = cos(2y + 20°), the value of tan(x + y) is?
Answer & Solution
Correct Answer:
Option
C
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
⇒ 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
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