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karina999
@karina999
August 2021
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Вычислите:
sin(2arcctgx)
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nelle987
Verified answer
Обозначим a = arcctg x. Тогда нужно найти sin 2a = 2 sin a cos a
x = ctg a; sin a = ?
ctg^2 x + 1 = 1 / sin^2 a
sin^2 a = 1/ (x^2 + 1)
sin a = +sqrt(...), если x > 0, и -sqrt(...), если x < 0
cos^2 a = 1 - sin^2 a = x^2 / (x^2 + 1)
cos a = | x | / sqrt(x^2 + 1)
sin 2a = 2x / (x^2 + 1)
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Answers & Comments
Verified answer
Обозначим a = arcctg x. Тогда нужно найти sin 2a = 2 sin a cos ax = ctg a; sin a = ?
ctg^2 x + 1 = 1 / sin^2 a
sin^2 a = 1/ (x^2 + 1)
sin a = +sqrt(...), если x > 0, и -sqrt(...), если x < 0
cos^2 a = 1 - sin^2 a = x^2 / (x^2 + 1)
cos a = | x | / sqrt(x^2 + 1)
sin 2a = 2x / (x^2 + 1)