April 20th, 2014, 04:24 AM  #1 
Senior Member Joined: Nov 2013 Posts: 434 Thanks: 8  complex
z = cos(x) + isin(x) prove that 2/(1z) = 1 + icot(x/2) Last edited by skipjack; April 20th, 2014 at 02:16 PM. Reason: to add parentheses 
April 20th, 2014, 02:11 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2202 
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. 
April 20th, 2014, 02:25 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2202 
Trigonometry problems should not normally be posted in the algebra subforum or the geometry subforum.


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