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MRMK
@MRMK
July 2022
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упростить выражение
sin^4 альфа-cos^4 альфа+cos^2альфа
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nafanya2014
Verified answer
Sin⁴α-cos⁴α+cos²α=(sin²α)²-(cos²α)²+cos²α=(sin²α-cos²α)(sin²α+cos²α)+cos²α=
=(sin²α-cos²α)·1+cos²α=sin²α-cos²α+cos²α=sin²α
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Answers & Comments
Verified answer
Sin⁴α-cos⁴α+cos²α=(sin²α)²-(cos²α)²+cos²α=(sin²α-cos²α)(sin²α+cos²α)+cos²α==(sin²α-cos²α)·1+cos²α=sin²α-cos²α+cos²α=sin²α