
Trigonometry Trigonometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 28th, 2017, 09:53 AM  #1 
Newbie Joined: Mar 2017 From: Azerbaijan Posts: 1 Thanks: 0  Help me with a very difficult question
(tan15°)×(tan25°)×(tan35°)×(tan85°) I know the answer, but I do not know the solution answer: 1 help me please. Last edited by skipjack; April 24th, 2017 at 08:56 PM. 
April 24th, 2017, 04:26 PM  #2 
Newbie Joined: Apr 2017 From: durban Posts: 9 Thanks: 0 Math Focus: Algebra 
* Joined: Mar 2017 From: Azerbaijan Posts: 1 Thanks: 0 Help me with a very difficult question (tan15°)×(tan25°)×(tan35°)×(tan85°) I know the answer but I do not know the solution answer: 1 help me please. It is very possible to get the value of 15 From special angle 45  30 and when solve will produce 2  root 3 but this process will nt work for 25, 35, and 85 Last edited by skipjack; April 24th, 2017 at 08:57 PM. 
April 24th, 2017, 04:32 PM  #3 
Newbie Joined: Apr 2017 From: durban Posts: 9 Thanks: 0 Math Focus: Algebra  Challenging Trigonometry Problems!? 1. If tan 15 tan 25 tan 35 = tan t, and t is between 0 and 180, find t. (All angle measures are in degrees.) 2. Find the number of solutions, in degrees, to the equation sin^10 x + cos^10 x = (29/16)cos^4 2x, where x is between 0 and 2007 degrees, inclusive. 3. Find both the maximum and minimum values of a) f(x) = sin x + cos x + tan x + csc x + sec x + cot x b) f(x) = sin x + cos x + tan x + csc x + sec x + cot x 
April 24th, 2017, 10:04 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 16,919 Thanks: 1253 
$\displaystyle \begin{align*}\tan15^\circ\tan25^\circ\tan35^\circ \tan85^\circ &= \frac{8\sin15^\circ\sin25^\circ\sin35^\circ\sin85^ \circ}{8\cos15^\circ\cos25^\circ\cos35^\circ\cos85 ^\circ} \\ &= \frac{(\cos10^\circ  \cos40^\circ)(2\cos50^\circ + 1)}{(\cos40^\circ + \cos10^\circ)(2\cos50^\circ  1)}\\ &= \frac{2\cos10^\circ\cos50^\circ + \cos10^\circ  2\cos40^\circ\cos50^\circ  \cos40^\circ}{2\cos40^\circ\cos50^\circ  \cos40^\circ + 2\cos10^\circ\cos50^\circ  \cos10^\circ} \\ &= \frac{2\cos10^\circ\cos50^\circ + \cos10^\circ  \cos10^\circ  \cos40^\circ}{\cos10^\circ  \cos40^\circ + 2\cos10^\circ\cos50^\circ  \cos10^\circ} \\ &= 1\end{align*}$ 
April 25th, 2017, 05:32 AM  #5 
Newbie Joined: Apr 2017 From: durban Posts: 9 Thanks: 0 Math Focus: Algebra 
That right skipjack. Dnt look at it from that corner


Tags 
difficult, question 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
difficult question  huy  Math  23  March 21st, 2017 08:15 PM 
Difficult question for me  student777  Math  1  January 11th, 2017 12:52 PM 
DIfficult Question, try it  Iamthatdude  Math Events  1  August 28th, 2013 12:13 PM 
difficult question  ahmedar  Calculus  3  December 9th, 2011 01:44 PM 
Difficult question!  DragonScion  Advanced Statistics  0  October 29th, 2011 02:54 PM 