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Мадина0009
@Мадина0009
November 2021
1
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(1-cos25+cos50)/(sin50-sin25) ×4tg65+3
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kalbim
Verified answer
Числитель дроби:
1 - cos25 + cos50 = 1 - cos25 + 2cos^2(25) - 1 = 2cos^2(25) - cos25 = cos25*(2cos25 - 1)
Знаменатель дроби:
sin50 - sin25 = 2sin25*cos25 - sin25 = sin25*(2cos25 - 1)
Дробь: cos25*(2cos25 - 1)/sin25*(2cos25 - 1) = cos25/sin25 = 1/tg25
Все выражение: (4tg65 + 3)/tg25 = (4tg(90 - 25) + 3)/tg25 = (4tg25 + 3)/tg25 = 4tg25/tg25 + (3/tg25) = 4 + (3/tg25) = 4 + 3ctg25
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Мадина0009
спасибо))
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Answers & Comments
Verified answer
Числитель дроби:1 - cos25 + cos50 = 1 - cos25 + 2cos^2(25) - 1 = 2cos^2(25) - cos25 = cos25*(2cos25 - 1)
Знаменатель дроби:
sin50 - sin25 = 2sin25*cos25 - sin25 = sin25*(2cos25 - 1)
Дробь: cos25*(2cos25 - 1)/sin25*(2cos25 - 1) = cos25/sin25 = 1/tg25
Все выражение: (4tg65 + 3)/tg25 = (4tg(90 - 25) + 3)/tg25 = (4tg25 + 3)/tg25 = 4tg25/tg25 + (3/tg25) = 4 + (3/tg25) = 4 + 3ctg25