A trig identity - Math Central

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Question from Julia, a student:

    sin4x              1 - cos2x
------------    x      ----------         =     tanx
1 - cos4x               cos2x

Hi Julia,

You need to use the double angle formulas

sin(2z) = 2 sin(z) cos(z)
cos(2z) = cos²(z) - sin²(z)

So in the first fraction for example

sin(4x) = 2 sin(2x) cos(2x) and
1 - cos(4x) = 1 - [cos²(2x) - sin²(2x)] = 1 - cos²(2x) + sin²(2x) = sin²(2x) + sin²(2x) = 2 sin²(2x)

I hope this helps,
Harley

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