Prove that the following Trigonometric Identity is valid:

Question

1/(sin⁡(y)-1)-1/(sin⁡(y)+1)=-2sec^2 (y)

Please any help or clues on how to do this is needed. I have a sheet that tells me valid identities but nowhere on it has info on -2sec^2 (y) I am sooo clueless here :(

Answer 1

LS = 1/(siny - 1) - 1/(siny + 1)
using a common denominator:

= (siny + 1 - (siny - 1)/( sin^2 y - 1)
= 2/(-cos^2 y)
= - 2 sec^2 y
= RS

Answer 2

THANK YOU REINY!!! however, what does RS mean?

Answer 3

LS ---> left side
RS ---> ???

Answer 4

ooohkay, thank you!! i needed this so bad :D