SOLUTION: please help me prove this statement: cotx=(1+sin2x+cos2x)/(1+sin2x-cos2x). i tried eliminating 1 by using double angle identities but i just got stuck after that.

Click here to see ALL problems on Trigonometry-basics

Question 443705: please help me prove this statement: cotx=(1+sin2x+cos2x)/(1+sin2x-cos2x). i tried eliminating 1 by using double angle identities but i just got stuck after that.
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
please help me prove this statement: cotx=(1+sin2x+cos2x)/(1+sin2x-cos2x). i tried eliminating 1 by using double angle identities but i just got stuck after that.
..
Start from right side
(1+sin2x+cos2x)/(1+sin2x-cos2x)
Identities used:
1=sin^2+cos^2
sin2x=2sinxcosx
cos2x=cos^2x-sin^2x
..
[sin^2x+cos^2x+2sinxcosx+cos^2x-sin^2x]/[sin^2x+cos^2x+2sinxcosx-cos^2x+sin^2x]
cancel out sin^2x in numerator and cancel out cos^2x in denominator
(2sinxcosx+2cos^2x)/(2sinxcosx+2sin^2x)
2cosx(sinx+cosx)/2sinx(cosx+sinx)
2cosx/2sinx=cotx
right side=left side