Question
If sin(A + B) = √3/2 and cos(A + 2B) = 1/2, where 0°
A, B < 90°, then find the value of tan(2A).Solution
sin(A + B) = √3/2
Or, sin(A + B) = sin 60°
Or, A + B = 60° -------- (I)
cos(A + 2B) = 1/2
Or, cos(A + 2B) = cos 60°
Or, A + 2B = 60° -------- (II)
On solving 2 × equation I – equation II,
We get, 2A + 2B − A − 2B = 120° − 60°
Or, A = 60°
Required value = tan(2A) = tan(120°) = -√3
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