SOLUTION: 2cos^2(x/2)=(sin^2x)/(1-cosx)

Algebra ->  Trigonometry-basics -> SOLUTION: 2cos^2(x/2)=(sin^2x)/(1-cosx)      Log On


   

Question 732417: 2cos^2(x/2)=(sin^2x)/(1-cosx)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Prove this identity:
2cos^2(x/2)=(sin^2x)/(1-cosx)
..
left side:
use cos half-angle formula:
2[√((1+cosx)/2)]^2=2((1+cosx)/2)=1+cosx
..
right side:(sin^2x)/(1-cosx)=(1-cos^2x)/(1-cosx)=%281%2Bcosx%29cross%281-cosx%29%2Fcross%281-cosx%29
verified:
left side=right side=1+cosx