WBJEE · Maths · Trigonometric Equations
If the equation \(\sin ^4 x-(p+2) \sin ^2 x-(p+3)=0\) has a solution, the \(p\) must lie in the interval
- A \([-3,-2]\)
- B \((-3,-2)\)
- C \((2,3)\)
- D \([-5,-3]\)
Answer & Solution
Correct Answer
(B) \((-3,-2)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \sin ^2 x=\frac{(P+2) \pm \sqrt{(P+2)^2+4.1(P+3)}}{2.1} \\ & =\frac{(P+2) \pm \sqrt{P^2+4 p+4+4 p+12}}{2} \\ & =\frac{(P+2) \pm \sqrt{(P+4)^2}}{2} \\ & =\frac{2 p+6}{2}=P+3 \\ & =\sin ^2 x \in[0,1] \\ 0 & \leq P+3 \leq 1 \\ & -3 \leq P \leq-2\end{aligned}\)
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