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.