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Limit of a difference of square roots of trig quadratics

This type of question, asked 2 times: 25 Jun 2022, 24 Jan 2025. All 2 questions below, oldest first.

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  1. Question 1

    25 Jun 2022

    155
     lim⁡x→π2(tan⁡2x((2sin⁡2x+3sin⁡x+4)12−(sin⁡2x+6sin⁡x+2)12))\ \lim_{x \rightarrow\frac{\pi}{2}} \left( \tan^{2}x\left( \left( 2\sin^{2}x + 3\sin x + 4 \right)^{\frac{1}{2}}-\left( \sin^{2}x + 6\sin x + 2 \right)^{\frac{1}{2}} \right) \right) is equal to

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  2. Question 2

    24 Jan 2025

    57
    lim⁡x→0csc⁡x(2cos⁡2x+3cos⁡x−cos⁡2x+sin⁡x+4)\lim_{x \rightarrow 0} \csc x\left( \sqrt{2\cos^{2}x + 3\cos x}-\sqrt{\cos^{2}x + \sin x + 4} \right) is

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