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ghostnight01
@ghostnight01
July 2022
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2 cos ²x - sin²x + 5 cos x - 1 = 0
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Spilrobe
2cos^2x - sin^2x + 5cosx - 1 =0
2cos^2x - sin^2x + 5cosx - sin^2x - cos^2x=0
cos^2x - 2sin^2x + 5cosx=0
заменяем sin^2x= 1-cos^2x через основное тригонометрическое тождество
cos^2x - 2(1-cos^2x) + 5cosx=0
cos^2x - 2 + 2cos^2x + 5cosx=0
3cos^2x + 5 cosx - 2=0
замена t=cosx
3t^2+5t-2=0
Д=7^2
t1=1/3
t2= -2
[cosx=1/3
[cosx=-2
[x=+- arccos1/3 + 2Пк, к € Z
[x € пустому множеству
2 votes
Thanks 1
Spilrobe
+- arccos1/3 + 2Пk, k € Z*
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Answers & Comments
2cos^2x - sin^2x + 5cosx - sin^2x - cos^2x=0
cos^2x - 2sin^2x + 5cosx=0
заменяем sin^2x= 1-cos^2x через основное тригонометрическое тождество
cos^2x - 2(1-cos^2x) + 5cosx=0
cos^2x - 2 + 2cos^2x + 5cosx=0
3cos^2x + 5 cosx - 2=0
замена t=cosx
3t^2+5t-2=0
Д=7^2
t1=1/3
t2= -2
[cosx=1/3
[cosx=-2
[x=+- arccos1/3 + 2Пк, к € Z
[x € пустому множеству