If sin(2x + 50)° = cos(2y - 50)°, such that 0° < x + y < 90°, then find the value of tan(x + y).
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Correct answer: C
Explanation
Given:
sin(2x + 50)° = cos(2y − 50)°
0° < x + y < 90°
By the formula:
sin θ = cos(90° − θ)
sin(2x + 50)° = cos(2y − 50)°
2x + 50 = 90 − (2y − 50)
2x + 50 = 140 − 2y
2x + 2y = 90
x + y = 45
tan(x + y)
= tan45°
= 1