In Exercises 1–60, verify each identity.

cos θ sec θ
----------...

Question

In Exercises 1–60, verify each identity.

cos θ sec θ 
----------------- = tan θ
cot θ

Accepted Answer

Hello, everybody. I hope you're doing tonight today. Today, we're going to look at this question that states determine the, determine whether the given identity is true or false where the given identity is open bracket, sign of M multiplied by C cans of M close bracket divided by C cans of M equals cosine. OK. Now, we only have two answer choices. A being true and B being false. Now, for a question like this, what I usually like to do or a question where we're trying to prove that this is true or false. What I usually like to do is tackle one side of the equation at a time. Now, in this case, all we have to prove is that the left hand side of our equation is equal to cosine of M. So let's try to just work with the left hand side and see if we can get to cosine of M. So focusing on the left hand side, let's first recall that cos cans of M is equal to one divided by sine of M. So we can rewrite to have open bracket sign of M multiplied by one divided by sin of M closed bracket and all that divided by C K M. Now, the sign of A in the, in the bracket inside the brackets will, the sign of MS will cancel out and we're going to be left with one divided by C cans. And, and we can recall that C cans of M is equal to one divided by cosine of M. So we can rewrite our equation as one divided by one divided by a cosine of M which just translates to cosine of. So at the end, we're left with cosine of M on the left hand side equals cosine of M on the right hand side which will be true and matches with answer choice A. So I hope that was helpful. And until next time.

In Exercises 1–60, verify each identity. cos θ sec θ ----------------- = tan θ cot θ

Key Concepts

Trigonometric Identities

Reciprocal Functions

Quotient Identity

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