Вычислите cos⁡50°-cos⁡40°∙ctg⁡115°

Question

Вычислите cos⁡50°-cos⁡40°∙ctg⁡115°

Comments

ответ 1

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а как решили

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подскажите пожалуйста

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cos50°-cos40°*ctg115°=(sin115°*cos50°-cos40°*cos115°)/sin115°==(sin115°*cos50°-cos(90°-50°)*cos115°)/sin(90°+25°)=(sin115°*cos50°-sin50°*cos115°)/cos25°==sin65°/cos25°=sin(90°-25°)/cos25°=cos25°/cos25°=1

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cos50 - cos40*ctg115. = cos50 - cos(90-50)*ctg(90+25) = . cos50 +sin50*tg25 =cos50 +(sin50*sin25)/ cos25 = (cos50cos25 +sin50*sih25)/ cos25 == cos(50-25)/cos25 = cos25/cos25 =1

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спасибо

Answer 1

Cos50 - cos40*ctg115
= cos50 - cos(90 - 50)*ctg(90 + 25) =
= cos50 + sin50*tg25 =
= cos50 +(sin50*sin25)/ cos25 =
 = (cos50cos25 + sin50*sin25)/ cos25 =
= cos(50-25)/cos25 =
 = cos25/cos25 = 1