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JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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Analyzing +4 | -1
For −π2<θ<π2,  sin⁡θ+sin⁡2θ1+cos⁡θ+cos⁡2θ- \frac{\pi }{2} < \theta < \frac{\pi }{2},\,\,\frac{{\sin \theta + \sin 2\theta }}{{1 + \cos \theta + \cos 2\theta }} lies in the interval
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Correct option: A
(−∞,   ∞)\left( { - \infty ,\;\,\infty } \right)
Option A is correct because the given expression simplifies to tan θ, and for -π/2 < θ < π/2, tan θ can take any real value.

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