Question
If x, y are acute angles, where 0 < x + y < 90° and sin(3x - 40°) = cos (3y + 40°), then the value of tan (x + y) is equal to
The correct answer is \(\frac{1}{\sqrt{3}}\)
Given:
sin(3x - 40°) = cos (3y + 40°)
Used Formula:
sinA = cosB
Then, A + B = 90°
Calculation:
sin(3x - 40°) = cos (3y + 40°)
⇒ 3x – 40° + 3y + 40° = 90°
⇒ 3x + 3y = 90°
⇒ x + y = 30°
Therefore, tan(x + y) = tan30° = 1/√3
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