Perform each transformation. See Example 2.
Write cot x ...

Question

Perform each transformation. See Example 2.

Write cot x in terms of csc x.

Accepted Answer

Welcome back. I am so glad you're here. We are asked to write the given trigonometric function in terms of the C can of X. And our given trigonometric function is the tangent of X. Our answer choices are answer choice A plus or minus the square rut of the C can't squared of X minus one answer. Choice B plus or minus the square root of one minus C can't squared X answer trace C plus or minus the square root of C can't squared X plus one and answer choice D plus or minus the square root of two C can squared X minus one. All right. So we've got the tangent of X and we need to get that to the C can of X. And we're going to use identities in order to get there specifically for this one. We are going to use a Pythagorean identity. We recall from previous lessons that the tangent squared of an angle here will use X plus one equals the C can squared of that same angle here. We're using X, there's a Pythagorean identity and what we have is similar to that but not quite the same. So we want to get our Pythagorean identity to look like our tangent of X on the left hand side, then we'll know what it's equal to in terms of the C can of X. So the first thing we're going to do is subtract one from both sides of the equation. Then on the left, it's looking closer, it's just the tangent squared of X almost there. Not quite that equals. And then on the right, we have the C can squared of X minus one. All right, to get rid of that tangent squared. So that it looks like just the tangent of X. We're going to take the square rut, what we do to one side we do to the other as well. So now on the left, we've got it, we've got just our tangent of X and that's equal to on the right, we took the square rut. So it's plus or minus and then it stays, it remains the square root of all of that C can't squared X minus one. We can't simplify that any further. So here is our tangent of X written in terms of the C can't of X. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Perform each transformation. See Example 2.
Write cot x in terms of csc x.

Key Concepts

Reciprocal Trigonometric Functions

Cosecant Function

Cotangent Function

Watch next