[tex]\frac{csc (x)}{cot (x)} = \sqrt{2}[/tex]
⇒ [tex]\frac{csc (x)}{1} * \frac{1}{cot (x)} = \sqrt{2}[/tex]
⇒ [tex]\frac{1}{sin (x)} * \frac{sin(x)}{cos (x)} = \sqrt{2}[/tex]
⇒[tex]\frac{1}{cos (x)} = \sqrt{2}[/tex] ; sin(x) ≠ 0, cos(x) ≠ 0
⇒ [tex]\frac{cos (x)}{1} = \frac{1}{\sqrt{2}}[/tex]; sin(x) ≠ 0, cos(x) ≠ 0
⇒ [tex]cos (x) = \frac{\sqrt{2}}{2}[/tex]
Use the Unit Circle to determine when [tex]cos (x) = \frac{\sqrt{2}}{2}[/tex]
Answer: 45° and 315° [tex](\frac{\pi}{4} and \frac{7\pi }{4} )[/tex]
