SOLUTION: Please Help!!!! Which of the following is equivalent to 1/(1-cos(x))- 1/(1+cos(x))? A) 2cot(x)csc(x) B) 2tan(x)sec(x) C) 2+cot^2(x) D) 4sec(4x) E) 0 When I subtract I get

Algebra.Com
Question 973828: Please Help!!!!
Which of the following is equivalent to 1/(1-cos(x))- 1/(1+cos(x))?
A) 2cot(x)csc(x)
B) 2tan(x)sec(x)
C) 2+cot^2(x)
D) 4sec(4x)
E) 0
When I subtract I get (1+cos(x))-(1-cos(x))/(1-cos(x))(1+cos(x)). That gives me 2cos(x)/1-cos^2(x). That's all I got. I can not figure where to go from here.
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Which of the following is equivalent to 1/(1-cos(x))- 1/(1+cos(x))?
A) 2cot(x)csc(x)
B) 2tan(x)sec(x)
C) 2+cot^2(x)
D) 4sec(4x)
E) 0
When I subtract I get
2cos(x)/1-cos^2(x)
= 2cos(x)/sin^2(x)
= 2(cos/sin)(1/sin)
= 2cot(x)*csc(x)

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
 
Remember the identity: ?
Subtract  from both sides and get   

The right side of that shows that the denominator of what you have so far
is 

 becomes:



Change the choices to all sines and cosines until you find
which one is equivalent.  Begin with A)

A) 2cot(x)csc(x)





So A) happens to be the correct choice.

We were lucky to get it on the first try.  If that had not
been the correct choice we would have changed the others to
sines and cosines, until we found the correct choice.

Edwin
RELATED QUESTIONS

Please Help!!!! Which of the following is equivalent to 1/(1-cos(x))- 1/(1+cos(x))? A)... (answered by Alan3354)
which of the following is equal to csc(x) A)1/sin(x) B)1/cos(x) C)1/tan(x)... (answered by Alan3354)
Find a numerical value of one trigonometric function of x if... (answered by lwsshak3)
I am given the expression: {{{ sec(x)*((sin(x))/(tan(x))) }}} Which of the following... (answered by math-vortex)
the expression (cot x)(sec x) is equivalent to ? (1) sin x (2) cos x (3) csc x (4)... (answered by jim_thompson5910)
Please help me solve this equation: Which of the following is a valid trigonometric... (answered by lwsshak3)
Choose the matching expression for -tan x cos x = A sin^2x/cos^2 x B. 1/sec^2 X... (answered by josgarithmetic,ikleyn)
Verify following is an identity.... (answered by Alan3354)
Prove each of the following trigonometric identities. 1) sin x sin 2x + cox x cos 2x = (answered by MathLover1)