Question

Given csc x/ cot x= √2, find a numerical value of one trigonometric function of x.

Answer 1

Choice A is correct.

Explanation:

We have given the equation:

csc x/ cot x= √2.

We have to find a numerical value of one trigonometric function of x.

As we know that,

cscx = 1/sinx and cotx = cosx /sinx we get,

1/sinx / cosx /sinx = √2

1/cosx = √2

secx = √2

sec x = √2 is the answer.

Answer 2

A

Explanation:

Note that

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

and

`\cot x=(\cos x)/(\sin x).`

Then

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

Since
`(\csc x)/(\cot x)=√(2),` you have that
`\sec x=√(2).`