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April 20th, 2014, 05:24 AM   #1
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complex

z = cos(x) + isin(x)

prove that
2/(1-z) = 1 + icot(x/2)

Last edited by skipjack; April 20th, 2014 at 03:16 PM. Reason: to add parentheses
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April 20th, 2014, 03:11 PM   #2
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cot(x/2) = (1 + cos(x))/sin(x), so
(1 - cos(x) - isin(x))(1 + i(1 + cos(x))/sin(x)) = 1 - cos(x) + (1 + cos(x)) - isin(x) + i(1 - cos²(x))/sin(x) = 2.
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April 20th, 2014, 03:25 PM   #3
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Trigonometry problems should not normally be posted in the algebra subforum or the geometry subforum.
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