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abieva
@abieva
August 2022
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помогите решить
в системе уравнений:
х+у=n/2
sin^2 x + cos^2 y = 1
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sedinalana
Verified answer
Х+у=n/2⇒x=π/2-y
sin^2 x + cos^2 y = 1
sin²(π/2-y)+cos²y=1
cos²y+cos²y=1
2cos²y=1
cos²y=1/2
(1+cos2y)/2=1/2
1+cos2y=1
cos2y=0
2y=π/2+πn
y=π/4+πn/2,n∈z
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Answers & Comments
Verified answer
Х+у=n/2⇒x=π/2-ysin^2 x + cos^2 y = 1
sin²(π/2-y)+cos²y=1
cos²y+cos²y=1
2cos²y=1
cos²y=1/2
(1+cos2y)/2=1/2
1+cos2y=1
cos2y=0
2y=π/2+πn
y=π/4+πn/2,n∈z