Question

решите уравнение: $\log_{\cfrac{4(ctg(\frac{\pi}{8})-1)(ctg(\frac{\pi}{8})+1)}{ctg^2(\frac{\pi}{8})+1}}64^{sinx}=2$

Answer 1

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
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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