Question

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

Answer 1

Answer: secx=
`√(2)`

Explanation:

A on edge

Answer 2

`(csc (x))/(cot (x)) = √(2)`

⇒
`(csc (x))/(1) * (1)/(cot (x)) = √(2)`

⇒
`(1)/(sin (x)) * (sin(x))/(cos (x)) = √(2)`

⇒
`(1)/(cos (x)) = √(2)` ; sin(x) ≠ 0, cos(x) ≠ 0

⇒
`(cos (x))/(1) = (1)/(√(2))`; sin(x) ≠ 0, cos(x) ≠ 0

⇒
`cos (x) = (√(2))/(2)`

Use the Unit Circle to determine when
`cos (x) = (√(2))/(2)`

Answer: 45° and 315°
`((\pi)/(4) and (7\pi )/(4) )`