How can this identity be proved/verified?
cscx-sinx=1/(secxtanx)
I have tried starting on both sides of the equation to get to the other. By starting on one side of the equation and manipulating it to make it look like the other side, the identity will be proved. However, this is where I'm stuck.
At first I tried to start on the right side because its harder to break up addition/subtraction, but I really have no idea what to do. Thanks to anyone that can help.
--Corin
usually the best way to do these is to change everything to sines and cosines, unless you recognize an obvious identity.
LS= 1/sinx - sinx
= (1-sin^2x)/sinx
= (cos^2x)/sinx (from sin^2x+cos^2x=1)
now do the RS
=(1/secx)(1/tanx)
=
I will let you finish it, it's not that hard from here.
Let me know if you got it.
Thanks so much! I got it. Only one problem now. I'm confused on the next problem. It is:
(Secx-1)/(1-cosx)=secx
I'm trying to start on the left. My teacher gave us a hint for this problem and said something about conjugate, but I can't figure out what to do.
Thanks for all your help.
ok, not that hard.
Don't know why your teacher mentioned conjugate, it has nothing to do with it.
LS= (1/cosx - 1)/(1-cosx)
=((1-cosx)/cosx)÷(1-cosx)
=(1-cosx)/cosx x 1/(1-cosx) and lo and behold, look what happens to 1-cosx !!
Very neat. Thanks again. I think I'm starting to get it now.
You're welcome! I'm glad you're starting to understand. The key to proving identities is often finding a way to manipulate one side of the equation to make it look like the other side. Sometimes it involves using trigonometric identities or simplifying expressions.
If you have any more questions or need further clarification, feel free to ask!