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am1re
@am1re
August 2022
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Довести тотожність/Доказать тождество
( Тригонометрия )
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sangers1959
Verified answer
Tg(α/2)/(1+tg(α/2))+tg(α/2)/(1-tg(α/2)=
=(tg(α/2)-tg²(α/2)+tg(α/2)+tg²(α/2)/(1-tg²(α/2))=2tg(α/2)/(1-sin²(α/2)/cos²(α/2)=
=2tg(α/2)/((cos²(α/2)-sin²(α/2))/cos²(α/2))=2tg(α/2)/(cosα/cos²(α/2))=
=2sin(α/2)*cos²(α/2)/(cos(α/2)*cosα)=sinα*cos(α/2)/(cos(α/2)*cosα)=
sinα/cosα≡tgα.
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Answers & Comments
Verified answer
Tg(α/2)/(1+tg(α/2))+tg(α/2)/(1-tg(α/2)==(tg(α/2)-tg²(α/2)+tg(α/2)+tg²(α/2)/(1-tg²(α/2))=2tg(α/2)/(1-sin²(α/2)/cos²(α/2)=
=2tg(α/2)/((cos²(α/2)-sin²(α/2))/cos²(α/2))=2tg(α/2)/(cosα/cos²(α/2))=
=2sin(α/2)*cos²(α/2)/(cos(α/2)*cosα)=sinα*cos(α/2)/(cos(α/2)*cosα)=
sinα/cosα≡tgα.