Question

Multiply; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent. (Attached)

Answer 1

\[4-4\cos ^2x\]

Answer 2

I guess you're not going to post the choices?

Answer 3

I'll post them in a second

Answer 4

A. 4 - cos^2x
B. 4 - 4cos^2x
C. 4sin^2x
D. (4)/(csc^2x)
E. (4)/(1 + cot^2x)

Answer 5

(2+2cos(x))(2-2cos(x))


2^2 - (2cos(x))^2


4 - 4cos^2(x)


So the original expression is equivalent to choice B. So choice B is NOT the answer (since we want something that is NOT equivalent)

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4 - 4cos^2(x)


4(1 - cos^2(x))


4*sin^2(x)


So the original expression is also equivalent to choice C. So choice B is NOT the answer

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4*sin^2(x)


4*(1/csc^2(x))


(4)/(csc^2(x))


So choice D is out as well


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(4)/(csc^2(x))


(4)/(1+cot^2(x))


and choice E is out


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So the only thing left is choice A, which is actually not equivalent to the original expression. You can see this if you plug in x = 0 into each expression and comparing the two results.

Answer 6

Thanks! That makes a lot more sense. Thanks for explaining.

Answer 7

sure thing