Question

Given cscx/cotx=sqrt2, find a numerical value of one trigonometric function of x.

Answer 1

   $\frac{csc (x)}{cot (x)} = \sqrt{2}$

⇒ $\frac{csc (x)}{1} * \frac{1}{cot (x)} = \sqrt{2}$

⇒ $\frac{1}{sin (x)} * \frac{sin(x)}{cos (x)} = \sqrt{2}$

⇒$\frac{1}{cos (x)} = \sqrt{2}$ ; sin(x) ≠ 0, cos(x) ≠ 0

⇒ $\frac{cos (x)}{1} = \frac{1}{\sqrt{2}}$; sin(x) ≠ 0, cos(x) ≠ 0

⇒ $cos (x) = \frac{\sqrt{2}}{2}$

Use the Unit Circle to determine when $cos (x) = \frac{\sqrt{2}}{2}$

Answer: 45° and 315°  $(\frac{\pi}{4} and \frac{7\pi }{4} )$

Answer 2

Answer: secx=$\sqrt{2}$

Step-by-step explanation:

A on edge