If , then lies…

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

If ∣1−∣sin⁡x∣1+sin⁡x∣≥23\left|1-\frac{|\sin x|}{1+\sin x}\right|\geq\frac23, then sin⁡x\sin x lies in (1) (−∞,−12]∪[12,∞)\left(-\infty,-\frac12\right]\cup\left[\frac12,\infty\right) (2) (−12,12)\left(-\frac12,\frac12\right) (3) [−12,12]\left[-\frac12,\frac12\right] (4) None of the above.

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