How do you verify the identity cosx-1=(cos2x-1)/(2(cosx+1))cosx−1=cos2x−12(cosx+1)?
1 Answer
Mar 30, 2017
Start with the right side:
(cos2x-1) / (2(cosx+1))cos2x−12(cosx+1)
Use the identity
(color(red)(2cos^2x-1)-1) / (2(cosx+1))2cos2x−1−12(cosx+1)
(2cos^2x - 2)/(2(cosx+1))2cos2x−22(cosx+1)
Now divide both the numerator and denominator by 2:
(cos^2x - 1) / (cosx + 1)cos2x−1cosx+1
Factor the numerator:
((cosx+1)(cosx - 1)) / (cosx + 1)(cosx+1)(cosx−1)cosx+1
((cancel(cosx+1))(cosx - 1)) / cancel(cosx+1)
cosx - 1
Which is the left side.
Final Answer