Question

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

Answer 1

Answer:

  a.  sec(x) = √2

Step-by-step explanation:

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

Answer 2

Answer:

The correct answer is a) $\sec(x) = \sqrt{2}$.

Step-by-step explanation:

Here we need to use some trigonometric identities:

• $\csc(x) = \frac{1}{\sin(x)}$,
• $\cot(x) = \frac{\cos(x)}{\sin(x)}$.

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

$\frac{\csc(x)}{\cot(x)} = \frac{\frac{1}{\sin(x)}}{\frac{\cos(x)}{\sin(x)}} = \frac{1}{\sin(x)}\frac{\sin(x)}{\cos(x)}$

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

$\frac{\csc(x)}{\cot(x)} = \frac{1}{\cos(x)} = \sec{x}$.

From here, the solutions is pretty straightforward.