Question
If cosec [180° − (3q/2) ] = √2, 0° < q < 90°, then find the value of {(2/√3) X cos q - 4 cos 3q}.
Solution
cosec [180° − (3q/2) ] = √2
Or, cosec (3q/2) = cosec 45 o [because cosec 45 o = √2, and cosec (180 - q) = cosec q]
Or, (3q/2) = 45 o
Or, q = 45 o X (2/3)
So, q = 30 o
(2/√3) cos q - 4 cos 3q = (2/√3) cos 30 o - 4 cos (3 X 30 o )
= (2/√3) X (√3/2) - 0 (because, cos 30 o = (√3/2) and cos 90 o = 0)
= 1
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