Question
If cosec (2A + B) = (2/√3) and cosec (A + B) = √2,
then determine the value of (4A - B).Solution
We have, cosec (2A + B) = (2/√3)
Or, cosec (2A + B) = cosec 60°
Or, 2A + B = 60° -------- (I)
And, cosec (A + B) = √2
Or, cosec (A + B) = cosec 45°
Or, A + B = 45° ------- (II)
On subtracting equation (II) from (I) ,
We have, (2A + B) - (A + B) = 60° - 45°
So, 'A' = 15°
Put the value of 'A' = 15° in equation (1) ,
So, 2(15°) + B = 60°
Or, 30° + B = 60°
So, 'B' = 30°
Therefore, required value = (4 X 15) - 30 = 30°
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