Question
If sin(A + B) = 1/2 and cos(A + 2B) = √3/2, where 0°
A, B < 90°, then find the value of tan(2A).Solution
sin(A + B) = 1/2
Or, sin(A + B) = sin 30°
Or, A + B = 30° -------- (I)
cos(A + 2B) = √3/2
Or, cos(A + 2B) = cos 30°
Or, A + 2B = 30° -------- (II)
On solving 2 × equation I – equation II,
We get, 2 × (A + B) − (A + 2B) = 2 × 30° − 30°
Or, 2A + 2B − A − 2B = 60° − 30°
Or, A = 30°
Required value = tan(2A) = tan(60°) = √3
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