Question:medium
If the equation \( \sin^4 x - (p + 2)\sin^2 x - (p + 3) = 0 \) has a solution, then \( p \) must lie in the interval:
If the equation \( \sin^4 x - (p + 2)\sin^2 x - (p + 3) = 0 \) has a solution, then \( p \) must lie in the interval:
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When dealing with trigonometric equations involving powers, substituting \( \sin^2 x = t \) (or \( \cos^2 x = t \)) simplifies the problem into solving a quadratic within a bounded domain \( [0,1] \).
Updated On: Nov 28, 2025
- \( [-3, -2] \)
- \( (-3, -2) \)
- \( (2, 3) \)
- \( [-5, -3] \)
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