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aqua3
@aqua3
July 2022
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решите пожалуйста 5 задание
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nKrynka
Решение
sin(α + π)/sin(α + 3π/2) + cos(3π - α)/[cos(π/2 + α) - 1] =
= - sinα / (- cosα) + (- cosα) / (- sinα - 1) =
= sinα / cosα + cosα / (1 + sinα) = [sinα * (1 + sinα) + cos²α] / [cosα*(1 + sinα)] =
= (sinα + sin²α + cos²α) / [cosα*(1 + sinα)] = (1 + sinα) /
/ [cosα*(1 + sinα)] =
= 1 / cosα
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Answers & Comments
sin(α + π)/sin(α + 3π/2) + cos(3π - α)/[cos(π/2 + α) - 1] =
= - sinα / (- cosα) + (- cosα) / (- sinα - 1) =
= sinα / cosα + cosα / (1 + sinα) = [sinα * (1 + sinα) + cos²α] / [cosα*(1 + sinα)] =
= (sinα + sin²α + cos²α) / [cosα*(1 + sinα)] = (1 + sinα) // [cosα*(1 + sinα)] =
= 1 / cosα