If , which of the following statements about is…

MATHEMATICS · Single correct · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

If 90∘<x<180∘90^{\circ}<x<180^{\circ}, which of the following statements about sin⁡2x\sin 2x is correct? (a) sin⁡2x\sin 2x is positive because 2x2x remains in the second quadrant where sine is positive. (b) sin⁡2x\sin 2x is negative because sin⁡x\sin x is positive and cos⁡x\cos x is negative. (c) sin⁡2x\sin 2x is positive since sin⁡2x=2sin⁡2x\sin 2x = 2\sin^{2}x and sin⁡x\sin x is positive. (d) sin⁡2x\sin 2x is zero because 2x=180∘2x=180^{\circ} when xx is the midpoint of the interval.

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