5sin^2x+14sinxcosx+8cos^2x=0...

julia23456789 @julia23456789

August 2022 1 7 Report

5sin^2x+14sinxcosx+8cos^2x=0

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KuOV

Verified answer

5sin²x + 14sinx·cosx + 8cos²x = 0 разделим обе части на cos²x≠0
5tg²x + 14tgx + 8 = 0
a = tgx
5a² + 14a + 8 = 0
D/4 = 7² - 5·8 = 49 - 40 = 9
a = (- 7 - 3)/5 = - 2 или a = (- 7 + 3)/5 = - 4/5 = - 0,8
tgx = - 2 tgx = - 0,8
x = - arctg 2 + πn, n∈Z x = - arctg 0,8 + πk, k∈Z

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