cos(a) ≠ 0
1 + 1/cos(a) + tg(a) = cos(a)/cos(a) + 1/cos(a) + sin(a)/cos(a) = (cos(a) + sin(a) + 1)/cos(a)
1 - 1/cos(a) + tg(a) = cos(a)/cos(a) - 1/cos(a) + sin(a)/cos(a) = (cos(a) + sin(a) - 1)/cos(a)
(cos(a) + sin(a) + 1) (cos(a) + sin(a) - 1) = (cos(a) + sin(a))² - 1 = cos²(a) + 2sin(a)cos(a) + sin²(a) - 1 = (cos²(a) + sin²(a) = 1) = 2sin(a)cos(a)
cos(a)*(1 + 1/cos(a) + tg(a))*(1 - 1/cos(a) + tg(a)) = cos(a) *2sin(a)cos(a)/ (cos(a)*cos(a)) = 2sin(a)
ответ А
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Answers & Comments
cos(a) ≠ 0
1 + 1/cos(a) + tg(a) = cos(a)/cos(a) + 1/cos(a) + sin(a)/cos(a) = (cos(a) + sin(a) + 1)/cos(a)
1 - 1/cos(a) + tg(a) = cos(a)/cos(a) - 1/cos(a) + sin(a)/cos(a) = (cos(a) + sin(a) - 1)/cos(a)
(cos(a) + sin(a) + 1) (cos(a) + sin(a) - 1) = (cos(a) + sin(a))² - 1 = cos²(a) + 2sin(a)cos(a) + sin²(a) - 1 = (cos²(a) + sin²(a) = 1) = 2sin(a)cos(a)
cos(a)*(1 + 1/cos(a) + tg(a))*(1 - 1/cos(a) + tg(a)) = cos(a) *2sin(a)cos(a)/ (cos(a)*cos(a)) = 2sin(a)
ответ А