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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 
Banned Camp Joined: Apr 2017 From: durban Posts: 22 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 
Banned Camp Joined: Apr 2017 From: durban Posts: 22 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: 18,962 Thanks: 1606 
$\displaystyle \begin{align*}\tan15^\circ\tan25^\circ\tan35^\circ \tan85^\circ &= \frac{8\sin15^\circ\sin25^\circ\sin35^\circ\sin85^ \circ}{8\cos15^\circ\cos25^\circ\cos35^\circ\cos85 ^\circ} \\ &= \frac{(\cos10^\circ  \cos40^\circ)(2\cos50^\circ + 1)}{(\cos40^\circ + \cos10^\circ)(2\cos50^\circ  1)}\\ &= \frac{2\cos10^\circ\cos50^\circ + \cos10^\circ  2\cos40^\circ\cos50^\circ  \cos40^\circ}{2\cos40^\circ\cos50^\circ  \cos40^\circ + 2\cos10^\circ\cos50^\circ  \cos10^\circ} \\ &= \frac{2\cos10^\circ\cos50^\circ + \cos10^\circ  \cos10^\circ  \cos40^\circ}{\cos10^\circ  \cos40^\circ + 2\cos10^\circ\cos50^\circ  \cos10^\circ} \\ &= 1\end{align*}$ 
April 25th, 2017, 05:32 AM  #5 
Banned Camp Joined: Apr 2017 From: durban Posts: 22 Thanks: 0 Math Focus: Algebra 
That right skipjack. Dnt look at it from that corner


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