How do you verify the identity #cosx-1=(cos2x-1)/(2(cosx+1))#?

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Answer 1 · 2017-03-30T00:14:05

Start with the right side:

#(cos2x-1) / (2(cosx+1))#

Use the identity #cos2x = color(red)(2cos^2x-1)#

#(color(red)(2cos^2x-1)-1) / (2(cosx+1))#

#(2cos^2x - 2)/(2(cosx+1))#

Now divide both the numerator and denominator by 2:

#(cos^2x - 1) / (cosx + 1)#

Factor the numerator:

#((cosx+1)(cosx - 1)) / (cosx + 1)#

#((cancel(cosx+1))(cosx - 1)) / cancel(cosx+1)#

#cosx - 1#

Which is the left side.

Final Answer