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slowlennes
@slowlennes
July 2022
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упростите sin² t - (cos²t)/ctg(-t)×tg t
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Vasily1975
Verified answer
Так как ctg(-t)=1/tg(-t), а tg(-t)=-tg(t), то и ctg(-t)=-1/tg(t). тогда (cos²t)/ctg(-t)*tg t =-cos²t, и выражение приводится к sin²t-(-cos²t)=sin²t+cos²t=1. Ответ: 1
2 votes
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slowlennes
Спасибо, Василий
Vasily1975
Желаю удачи!
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Answers & Comments
Verified answer
Так как ctg(-t)=1/tg(-t), а tg(-t)=-tg(t), то и ctg(-t)=-1/tg(t). тогда (cos²t)/ctg(-t)*tg t =-cos²t, и выражение приводится к sin²t-(-cos²t)=sin²t+cos²t=1. Ответ: 1