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lenatavkhitova
@lenatavkhitova
September 2021
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Решить неравенство | sin x + cos x |<√2/2
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sedinalana
Verified answer
Sinx+cosx=sinx+sinx(π/2-x)=2sinπ/4cos(x-π/4)=√2cos(x-π/4)
√2|cos(x-π/4)\<√2/2
|cos(x-π/4)|<1/2
-1/2<cos(x-π/4)<1/2
π/3+2πn<x-π/4<2π/3+2πn U 4π/3+2πn<x-π/4<5π/3+2πn
7π/12+2πn<x<11π/12+2πn U 19π/12+2πn<23π/12+2πn,n∈z
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Answers & Comments
Verified answer
Sinx+cosx=sinx+sinx(π/2-x)=2sinπ/4cos(x-π/4)=√2cos(x-π/4)√2|cos(x-π/4)\<√2/2
|cos(x-π/4)|<1/2
-1/2<cos(x-π/4)<1/2
π/3+2πn<x-π/4<2π/3+2πn U 4π/3+2πn<x-π/4<5π/3+2πn
7π/12+2πn<x<11π/12+2πn U 19π/12+2πn<23π/12+2πn,n∈z