 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: 111 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: 7,683 Thanks: 2664 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: 111 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: 20,972 Thanks: 2222 Other correct answers are cot 60.13 degrees, etc. Tags application, demonstration, halfangle, identity Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post swm06 Algebra 5 May 10th, 2012 08:50 PM suomik1988 Algebra 1 November 29th, 2009 08:13 PM stef975_2009 Algebra 3 October 22nd, 2009 09:08 PM mikeportnoy Algebra 5 November 14th, 2008 02:18 AM BobDole2000 Algebra 3 March 27th, 2008 11:38 AM

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