Question

Prove 1/1-cosx + 1/1+cosx = 2csc^2x, use left to start proof...please help

Answer 1

Try to combine them in one denominator. :)

Answer 2

would the denominator be 1-cosx^2?

Answer 3

Yup.

Answer 4

So what do you do after you get 2/1-cosx^2?

Answer 5

From pythagorean identity: sin^2x + cos^2 = 1
What can you say with that?

Answer 6

so you change the cosx^2 to sin?

Answer 7

yep. 1-cos^2x = sin^2x :)

Answer 8

And from the ratio identity 1/sin = csc

Answer 9

Have you proven it now?

Answer 10

wait but wasnt it when you got the common denominator you added them together so on the top wouldnt there be a 2 instead of a 1?

Answer 11

I didn't get your question.

Answer 12

hopefully this makes sense so in the original problem the numerators are 1 and when I found the common denominator, i did 1/1-cosx^2 +1/1-cosx^2. So wouldnt that give me 2/1-cosx^2?

Answer 13

You're right.
But it should be\[\frac{ 2 }{ 1-\cos^2 x }\]

Answer 14

yeah, so when you put sin on the bottom it turns into 2/sin^2x and then the sin turns into csc and the 2 moves down?

Answer 15

Nope. It's like \[2(\frac{ 1 }{ \sin^2x })\]

Answer 16

Hence, it will also be like \[2(\csc^2 x)\]
which will yield to \[2\csc^2 x\]

Answer 17

But how did you move the 2 down...did you multiply?