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skvrttt
@skvrttt
July 2022
1
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решите уравнение: [tex]\log_{\cfrac{4(ctg(\frac{\pi}{8})-1)(ctg(\frac{\pi}{8})+1)}{ctg^2(\frac{\pi}{8})+1}}64^{sinx}=2[/tex]
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sedinalana
4(ctg(π/8)-1)(ctg(π/8)+1)/(ctg²(π/8)+1)=4(ctg²(π/8)-1)/(ctg²π/8)+1)=
=4(cos²(π/8)-sin²(π/8))/(cos²(π/8)+sin²(π/8))=4cos(π/4)=2√2
--------------------------
log(2√2)(64^sinx)=2
64^sinx=8
8^2sinx=8
2sinx=1
sinx=1/2
x=π/6+2πk U x=5π/6+2πk,k∈z
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Answers & Comments
=4(cos²(π/8)-sin²(π/8))/(cos²(π/8)+sin²(π/8))=4cos(π/4)=2√2
--------------------------
log(2√2)(64^sinx)=2
64^sinx=8
8^2sinx=8
2sinx=1
sinx=1/2
x=π/6+2πk U x=5π/6+2πk,k∈z