Question

Given csc x/cot x =square root 2, find a numerical value of on trigonometric function of x

Answer 1

The correct answer is a)
`\sec(x) = √(2)`.

Explanation:

Here we need to use some trigonometric identities:

• 
  `\csc(x) = (1)/(\sin(x))`,
• 
  `\cot(x) = (\cos(x))/(\sin(x))`.

Then, substituting the above identities in the given formula we have:

`(\csc(x))/(\cot(x)) = ((1)/(\sin(x)))/((\cos(x))/(\sin(x))) = (1)/(\sin(x))(\sin(x))/(\cos(x))`

Notice that we can simplify the sinus in both fractions. Thus,

`(\csc(x))/(\cot(x)) = (1)/(\cos(x)) = \sec{x}`.

From here, the solutions is pretty straightforward.

Answer 2

a. sec(x) = √2

Explanation:

csc(x)/cot(x) = (1/sin(x))/(cos(x)/sin(x)) = 1/cos(x) = sec(x) = √2