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January 15th, 2019, 06:47 AM  #1 
Senior Member Joined: May 2014 From: Allentown PA USA Posts: 110 Thanks: 6 Math Focus: dynamical systen theory  A Demonstration of an application of a halfangle identity
Dear My Math Forum Community: Express this as a single trigonometric function: (1  cos 59.74 degrees)/sin 59.74 degrees The correct answer is: tan 29.87 degrees. Could someone please provide me with a stepbystep demonstration as to how the answer is arrived at? Thank you. Last edited by skipjack; January 16th, 2019 at 04:24 AM. 
January 15th, 2019, 07:39 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,664 Thanks: 2643 Math Focus: Mainly analysis and algebra 
\begin{align} \frac{1  \cos 2\theta}{\sin 2\theta} &= \frac{1  (\cos^2 \theta  \sin^2 \theta)}{2\sin \theta \, \cos \theta} \\ &= \frac{1  (1  2\sin^2 \theta)}{2\sin \theta \, \cos \theta} \\ &= \frac{\cancel{2}\sin^\cancel{2} \theta}{\cancel{2}\cancel{\sin \theta} \, \cos \theta} \\ &= \frac{\sin \theta}{\cos \theta} \\ &= \tan \theta \\ \end{align} 
January 15th, 2019, 03:04 PM  #3 
Senior Member Joined: May 2014 From: Allentown PA USA Posts: 110 Thanks: 6 Math Focus: dynamical systen theory  to V8archie
Thanks for the proof! I was so intent on specifics that I overlooked the generalities of the situation.

January 16th, 2019, 04:22 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,753 Thanks: 2136 
Other correct answers are cot 60.13 degrees, etc.


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application, demonstration, halfangle, identity 
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