Question Number 195097 by Rupesh123 last updated on 24/Jul/23
Answered by Rasheed.Sindhi last updated on 24/Jul/23
$$\mathrm{49}^{\mathrm{sin}\:{x}} =\sqrt[{\mathrm{cos}\:{x}}]{\mathrm{7}}\: \\ $$$$\mathrm{7}^{\mathrm{2}\:\mathrm{sin}\:{x}} =\mathrm{7}^{\frac{\mathrm{1}}{\mathrm{cos}\:{x}}} \\ $$$$\mathrm{2}\:\mathrm{sin}\:{x}=\frac{\mathrm{1}}{\mathrm{cos}\:{x}} \\ $$$$\mathrm{2}\:\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}=\mathrm{1} \\ $$$$\:\mathrm{sin}\:\left(\mathrm{2}{x}\right)=\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{2}{x}=\frac{\pi}{\mathrm{2}}+\mathrm{2}{n}\pi \\ $$$$\:\:\:\:\:\:\:\:\:{x}=\frac{\pi}{\mathrm{4}}+{n}\pi \\ $$
Commented by Rupesh123 last updated on 24/Jul/23
Nice!