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

Question

Perform each transformation. See Example 2.

Write cot x in terms of sin x.

Accepted Answer

Hello, everyone. We are asked to write the given trigonometric function. In terms of the cosine of X, we are asked to rewrite the tangent of X. Our answer choices are a plus or minus the square root of one plus the cosine squared of X all which is divided by the cosine of X B plus or minus the square root of the cosine squared of X minus one, all of which is divided by the cosine of X C plus or minus the square root of one minus the cosine squared of X all of which is divided by one plus the cosine squared of X D plus or minus the square root of one minus the cosine squared of X, all of which is divided by the cosine of X. First, let's get this as in terms of cosign as we can without doing anything that requires a lot of moving to start with. So I recall that the tangent of acts could be rewritten as the sine of X divided by the cosine of X. So in this, we already are halfway there, we're already halfway to cosine. Next, I need to replace the sign of X. So using a Pythagorean identity, I know that the sine of X is equal to plus or minus the square root of one minus the cosine squared of X. So I'm going to put that square root in for the sin of X. So in my numerator, I will have plus or minus the square root of one minus the cosine squared of X divided by our denominator, which was our cosine of X. So I could pull the plus or minus out front and rewrite this. So my numerator is the square root of one minus the cosine squared of X. My denominator is the cosine of X and we've done it, we have rewritten the tangent of X in terms of cosine and we have plus or minus the square root of one minus the cosine squared of X all which is divided by the cosine of X. And that's answer choice. D have a nice day.

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