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Limit of sin or tan of pi times a power of cos

This type of question, asked 2 times: 2021 Paper 8, 2021 Paper 22. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 8

    77
    The value of the limit lim⁡θ→0tan⁡(πcos⁡2θ)sin⁡(2πsin⁡2θ)\lim_{\theta\rightarrow 0} \frac{\tan\left( \pi\cos^{2}\theta \right)}{\sin\left( 2\pi\sin^{2}\theta \right)} is equal to :

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  2. Question 2

    2021 Paper 22

    77
    lim⁡x→0sin⁡2(πcos⁡4x)x4\lim_{x\rightarrow 0} \frac{\sin^{2}\left( \pi\cos^{4}x \right)}{x^{4}} is equal to:

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