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alisa21b
@alisa21b
March 2022
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Доказать тождество. На первый пример
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sangers1959
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A) ((sinα+cosα)²-1)/(tgα-sinα*cosα)
(sin²α+2*sinα*cosα+cos²α-(sin²α+cos²α)/(sinα/cosα-sinα*cosα)=
=2*sinα*cosα/(sinα*(1/cosα-cosα)=2*sinα*cosα/((sinα*(1-cos²α))/cosα)=
=2*sinα*cosα/(sinα*sin²α/cosα)=2*sinα*cos²α/sin³α=2*cos²α/sin²α=2*ctg²α.
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Verified answer
A) ((sinα+cosα)²-1)/(tgα-sinα*cosα)(sin²α+2*sinα*cosα+cos²α-(sin²α+cos²α)/(sinα/cosα-sinα*cosα)=
=2*sinα*cosα/(sinα*(1/cosα-cosα)=2*sinα*cosα/((sinα*(1-cos²α))/cosα)=
=2*sinα*cosα/(sinα*sin²α/cosα)=2*sinα*cos²α/sin³α=2*cos²α/sin²α=2*ctg²α.