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Question Number 139141 by bramlexs22 last updated on 23/Apr/21

$$3^{\sin \mathrm{x}}\cos \mathrm{x}-3^{\cos \mathrm{x}}\sin \mathrm{x}=0$$

Answered by phanphuoc last updated on 23/Apr/21

$$\frac{3^{sinx}}{sinx}=\frac{3^{cosx}}{cosx}\to sinx=cosx\to tgx=1\to x=\pi /4+k\pi$$$$sinxcosx=0\to sin2x=0\to 2x=k\pi \to x=k\pi /2$$

Commented by mr W last updated on 23/Apr/21

$$x\ne \frac{k\pi }{2}$$

Answered by EDWIN88 last updated on 23/Apr/21

$$\mathrm{x}=\frac{\pi }{4}\mathrm{\&}\mathrm{x}=\frac{5\pi }{4}$$

Commented by mr W last updated on 23/Apr/21

$$ithinkgenerallyx=k\pi +\frac{\pi }{4}$$

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