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Question Number 151742 by mnjuly1970 last updated on 22/Aug/21

$$$$$$\mathrm{F}\left(x\right):=\frac{log(sin\left(x\right)+cos\left(x\right))}{log\left(sin\left(2x\right)\right)}$$$$findtheDomainof\mathrm{F}...$$$${\mathrm{D}}_{\mathrm{F}}=?$$

Answered by mindispower last updated on 22/Aug/21

$$F(x+2\pi )=F\left(x\right)$$$$wecanstudyfin[0,2\pi [$$$$sin\left(2x\right)>0\Rightarrow x\in ]0,\frac{\pi }{2}[$$$$sin\left(x\right)+cos\left(x\right)=\sqrt{2}sin(x+\frac{\pi }{4})>0\Rightarrow x\in ]-\frac{\pi }{4},\frac{3\pi }{4}[$$$$DF=]0,\frac{\pi }{2}[$$

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