## Fundamental Identities

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.

### Fundamental Identities

can everyone help solving my problem i cant understand please any one...

COTx + TANx = 2COSx CSCx - SECx CSCx

lorst789

Posts: 3
Joined: Mon Jul 29, 2013 2:48 pm

### Re: Fundamental Identities

lorst789 wrote:i cant understand....

COTx + TANx = 2COSx CSCx - SECx CSCx

What were the instructions? Are you supposed to solve via the use of fundamental trig identities, or is this an identity itself and you are needing to prove it? Which part are you not understanding?
nona.m.nona

Posts: 255
Joined: Sun Dec 14, 2008 11:07 pm

### Re: Fundamental Identities

i need to prove it.. sorry i forgot to put it
lorst789

Posts: 3
Joined: Mon Jul 29, 2013 2:48 pm

### Re: Fundamental Identities

lorst789 wrote:Prove:

COTx + TANx = 2COSx CSCx - SECx CSCx

This site offers a lesson on proving trigonometric identities; you may access that lesson here.

The lesson recommends starting with the "messier" side of the equation which, in this case, would be the right-hand side (RHS). Another recommendation is to convert each trigonometric function to its equivalent in sine and cosine. This would create the following:

RHS = 2cos(x)csc(x) - sec(x)csc(x)
RHS = 2cos(x)[1/sin(x)] - [1/cos(x)][1/sin(x)]

Then combine and apply identities, as possible:

RHS = 2[cos(x)/sin(x)] - 1/[cos(x)sin(x)]
RHS = 2cos^2(x)/[cos(x)sin(x)] - 1/[cos(x)sin(x)]
RHS = [2cos^2(x) - 1]/[cos(x)sin(x)]

And so forth. If you are unable to complete this exercise, kindly please reply showing your steps, starting from what has been displayed for you above. Thank you.
nona.m.nona

Posts: 255
Joined: Sun Dec 14, 2008 11:07 pm