My Math Forum A Demonstration of an application of a half-angle identity

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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 half-angle 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 step-by-step 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: 7,635 Thanks: 2620 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} Thanks from jonah, greg1313, topsquark and 1 others
 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: 20,469 Thanks: 2038 Other correct answers are cot 60.13 degrees, etc.

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