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DaxDino
@DaxDino
July 2022
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Уравнение. 30 баллов
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армения20171
(√(1+sinx)-√(1-sinx))²=(1+cosx)²;(sinx+1>0;
1-sinx>0)
1+sinx-2√(1-sin²x)+1-sinx=1+2cosx+cos²x
2-2cosx-1-2cosx-cos²x=0
-cos²x-4cosx+1=0
cos²x+4cosx-1=0;cosx=t€[-1;1]
t²+4t-1=0
D=16+4=20
t=(-4±2√5)/2=(-2±√5)
cosx=-2-√5;нет решения
cosx=(√5)-2
x=±arccos((√5)-2)+2πk;k€Z
2)1+cosx=0
cosx=-1
x=π+2πk;k€Z
1 votes
Thanks 1
DaxDino
x=2пи*n+пи подходит также
армения20171
да
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Answers & Comments
1-sinx>0)
1+sinx-2√(1-sin²x)+1-sinx=1+2cosx+cos²x
2-2cosx-1-2cosx-cos²x=0
-cos²x-4cosx+1=0
cos²x+4cosx-1=0;cosx=t€[-1;1]
t²+4t-1=0
D=16+4=20
t=(-4±2√5)/2=(-2±√5)
cosx=-2-√5;нет решения
cosx=(√5)-2
x=±arccos((√5)-2)+2πk;k€Z
2)1+cosx=0
cosx=-1
x=π+2πk;k€Z