If the angles A, B, C of a triangle are in arithmetic progression such that sin(2A + B) = 1/2 then sin(B + 2C) is equal to
Explanation:
Let the three angle of the triangle be A = a - d, B = a and C = a + d degrees. ⇒ A + B + C = (a - d) + a + (a + d) = 180° ⇒ a = 60°
∴ B = 60°
Now, Sin(2A + B) = 1/2 Since, B = 60° (2A + B) > 60° Sin30° = 1/2 or Sin(180 - 30) = 1/2 ⇒ 2A + B = 180 - 30 ⇒ 2A + 60° = 150° ⇒ A = 45°
∴ C = 180 - 45 - 60 = 75°
∴ Sin(B + 2C) = Sin(210°) = Sin(180° + 30°) = - Sin(30°) = - 1/2
Hence, option (a).
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