Mathematics
OpenStudy (anonymous):

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

OpenStudy (anonymous):

OpenStudy (mertsj):

$4-4\cos ^2x$

OpenStudy (mertsj):

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

OpenStudy (anonymous):

I'll post them in a second

OpenStudy (anonymous):

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

jimthompson5910 (jim_thompson5910):

(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) --------------------------------------- 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 --------------------------------------- 4*sin^2(x) 4*(1/csc^2(x)) (4)/(csc^2(x)) So choice D is out as well ---------------------------------------- (4)/(csc^2(x)) (4)/(1+cot^2(x)) and choice E is out ================================ 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.

OpenStudy (anonymous):

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

jimthompson5910 (jim_thompson5910):

sure thing