UPSC NDA I 2023 Mathematics Solved Paper

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Consider the following for the next two (02) items that follow :
Let sin‌β be the GM of sin‌α and cos‌α;tan‌γ be the AM of sin‌α and cos‌α.
[NDA I 2023]
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What is cos‌2‌β equal to ?
[NDA I 2023]
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