
Trigonometry Trigonometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 15th, 2019, 07:47 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 05:24 AM. 
January 15th, 2019, 08:39 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,598 Thanks: 2583 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, 04:04 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, 05:22 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,262 Thanks: 1958 
Other correct answers are cot 60.13 degrees, etc.


Tags 
application, demonstration, halfangle, identity 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Half Angle Identity  swm06  Algebra  5  May 10th, 2012 09:50 PM 
what half angle identity would I use?  suomik1988  Algebra  1  November 29th, 2009 09:13 PM 
halfangle identity help?  stef975_2009  Algebra  3  October 22nd, 2009 10:08 PM 
half angle ..  mikeportnoy  Algebra  5  November 14th, 2008 03:18 AM 
Halfangle trouble  BobDole2000  Algebra  3  March 27th, 2008 12:38 PM 