Решите уравнение 2tg^2 x+tgx-1=0. Created by kolap0697. matematika-ru

Решите уравнение 2tg^2 x+tgx-1=0...

kolap0697 @kolap0697

July 2022 1 17 Report

Решите уравнение 2tg^2 x+tgx-1=0

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afet74

Ответ:

Пошаговое объяснение:

2tg² x+tgx-1=0

tgx=t

2t²+t-1=0

$t=\frac{-1\frac{+}{}\sqrt{1+8} }{4} =\frac{-1\frac{+}{} 3}{4} \\\\t_{1} =\frac{-1-3}{4} =-1\\\\t_2=\frac{-1+3}{4} =\frac{1}{2}\\\\tgx=-1\\x=\frac{\pi }{4} +\pi k, \\\\tgx=\frac{1}{2} \\\\x=arctg(\frac{1}{2}) +\pi k$

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