Answer: [tex]x = \frac{\pi}{4}\pm k\frac{\pi}{2}\,\,\,\,\,\,k=\{0,1,2,...\}[/tex]
Step by step:
[tex]1 + 5\sin^2x= 7\sin^2x\\\sin^2 x\rightarrow z\\1 + 5z = 7z\\2z = 1\\z = \frac{1}{2}\implies \sin^2 x = \frac{1}{2}\\|\sin x| = \frac{1}{\sqrt{2}}\\\sin x = \pm\frac{1}{\sqrt{2}}=\pm\frac{\sqrt{2}}{2}\\\implies x = \frac{\pi}{4}\pm k\frac{\pi}{2}\,\,\,\,\,\,k=\{0,1,2,...\}[/tex]
(Used a table of common angles)
