Question
If cosec (2A + B) = 1 and cosec (A + B) = (2/√3), find
the value of (4A – B).Solution
We have, cosec (2A + B) = 1
Or, cosec (2A + B) = cosec 90°
Or, 2A + B = 90° -------- (I)
And, cosec (A + B) = (2/√3)
Or, cosec (A + B) = cosec 60°
Or, A + B = 60° ------- (II)
On subtracting equation (II) from (I),
We have, (2A + B) – (A + B) = 90° – 60°
So, A = 30°
Put the value of A = 30° in equation (II),
So, 30° + B = 60°
Or, B = 30°
Therefore, required value = (4 × 30°) – 30° = 90°
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