If 3 sin x + 4 cos x = 2, then the value of 3 cos x - 4 sin x is equal to:
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Correct answer: B
Explanation
The correct answer is option 2 i.e. √21
3 sin x + 4 cos x = 2
On squaring both sides we get,
9sin2x + 16cos2x + 24 sinx cosx = 4.......(1)
3 cos x - 4 sin x = a
On squaring both sides we get,
9cos2x + 16sin2x - 24sinx cosx = a2 .......(2)
On adding 1 and 2 we get,
25(sin2x + cos2x) = 4 + a2
a2 = 21
a = √21.