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

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