The set of all real value of \(p\) for which the equation \(3 \sin^2x + 12 \cos x - 3 = p\) has at least one solution is
Question and options
The set of all real value of for which the equation has at least one solution is
Answer and explanation
Correct answer: C - \([-15, 9]\)
3sin^2x+12cosx-3 = -3cos^2x+12cosx = -3c^2+12c with c in [-1,1]. This is increasing on [-1,1] (vertex at c=2): from -15 at c=-1 to 9 at c=1. Range [-15,9].
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