For each expression in Column I, choose the expression from Co...

Question

For each expression in Column I, choose the expression from Column II that completes an identity. One or both expressions may need to be rewritten.

sec x/csc x

Accepted Answer

Hey, everyone in this problem we're asked which of the following expressions is equivalent to cosine of X multiplied by cos can of X are given four answer choices, option A tangent squared of X, option B negative sine of X, option C cotangent of X and option D tangent of X. So let's start by writing our expression out cosine of X multiplied by cosecant of X. We're just gonna simplify as much as we can. OK. So we're gonna take cos can we know that that's a reciprocal trig function. And we're gonna write it in terms of the more basic trig functions that we're used to dealing with sine cosine. OK. So we can write this expression as cosine of X multiplied by one divided by sine of X. Mhm All right. Now, just doing some algebra simplifying and writing this as one fraction. We have cosine of X divided by sine of X. Now, you might notice right away that cosine of X divided by sine of X is just cotangent of X. OK. Now, if you didn't notice that we're gonna show a couple of steps to help you get. OK. So if you didn't notice that, well, you could look at this and know that sine of X divided by cosine of X is tangent of X. So we write our fraction as one divided by sine of X divided by cosine of X. And that's an equivalent expression. And then we know our denominator is tangent of X. So this becomes one divided by tangent of X and one divided by tangent of X. The reciprocal of tangent is just cotangent of X. OK. So you may have remembered that cotangent of X is cosine divided by S and you could have gone straight from that second line to that answer choice. But if you didn't, you can still work this out by going through the steps to turn this into something related to tangent. And then knowing that the reciprocal of that tangent function is cotangent. All right. So we found that cosine of X multiplied by Cosan of X is equivalent to cotangent of X. So the correct answer here is option C Thanks everyone for watching. I hope this video helped see you in the next one.

For each expression in Column I, choose the expression from Column II that completes an identity. One or both expressions may need to be rewritten.
sec x/csc x

Key Concepts

Reciprocal Trigonometric Functions

Simplifying Trigonometric Expressions

Trigonometric Identities

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