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.

-tan x cos x

II

A. sin ^2 x/cos ^2 x

B.1/(sec ^2 x)

C. sin (-x)

D. csc ^2 x-cot ^2 x + sin ^2 x

E. tan x

Accepted Answer

Hey, everyone in this problem we're asked which of the following expressions is equivalent to negative cotangent X multiplied by sin of X. We have four answer choices. Option A negative cosine of X, option B cosine of X, option C negative sine of X and option D tangent of X. So let's start with the expression that we're given in the problem negative cotangent of X multiplied by sin. OK. And we can see from the answer choices that these are written as either cosine sine tangent. OK. So we wanna break what we're given down into those more basic elementary trigonometric functions. OK? So we know that code tangent of X is a reciprocal trig function. So let's instead of writing code tangent of X, write it as one divided by tangent of X. OK. So our expression becomes negative one divided by tangent of X multiplied by sine effects. OK. Now tangent, we know we can break up a sine divided by cosine. But let's go ahead and do that. We get negative one divided by sine of X divided by cosine of X multiplied by side effects. OK? Simplifying that first fraction, we can write this as negative cosine of X divided by sin of X multiplied by sin of effects. And now these two sine X terms are going to divide out. We're gonna be left with just negative cosine of X. OK. And so we just broke down that original expression into more basic trig functions simplified. And we found that negative cotangent of X multiplied by sine of X is equivalent to negative cosine of X. And so the correct answer is option A 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.
-tan x cos x

II
A. sin ^2 x/cos ^2 x
B.1/(sec ^2 x)
C. sin (-x)
D. csc ^2 x-cot ^2 x + sin ^2 x
E. tan x

Key Concepts

Trigonometric Identities

Relationship Between Tangent, Sine, and Cosine

Algebraic Manipulation of Trigonometric Expressions

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