 My Math Forum Determine values of variables for each of the following identities

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 April 21st, 2018, 06:39 AM #1 Newbie   Joined: Apr 2018 From: East London Posts: 12 Thanks: 0 Determine values of variables for each of the following identities 1. 2x / Cosx- Sinx = Cosx + Sinx 2.1 - Sin 2x / Sinx- Cosx = Sinx - Cosx 3.Sinx + Sinx /1 + Cosx + Cos2x = Tanx Last edited by greg1313; April 21st, 2018 at 01:36 PM. April 21st, 2018, 07:10 AM #2 Senior Member   Joined: Oct 2009 Posts: 811 Thanks: 306 2. $$1-\frac{\sin(2x)}{\sin(x)} - \cos(x)=\sin(x)-\cos(x)$$ if and only if $$1-\frac{2\sin(x)\cos(x)}{\sin(x)} = \sin(x)$$ if and only if $$1-2\cos(x) = \sin(x)$$ Letting $$t=\tan(x/2)$$, we get $$1-2\frac{1-t^2}{1+t^2} = \frac{2t}{1+t^2}$$ if and only if $$1+t^2 - 2+2t^2 = 2t$$ if and only if $$3t^2 - 2t-1=0$$ Discriminant is $$D=7$$ So $$t = \frac{2\pm \sqrt{7}}{6}$$ So $$x = 2\text{arctan}\left(\frac{2\pm \sqrt{7}}{6}\right)$$ Now I'm sure you can do the rest in the same way! Last edited by skipjack; April 26th, 2018 at 08:28 AM. April 21st, 2018, 10:00 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,757 Thanks: 2138 The second equation lacked parentheses; it should have been $\frac{1 - \sin 2x}{\sin x - \cos x} = \sin x - \cos x$. Thanks from topsquark April 21st, 2018, 01:38 PM   #4
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Quote:
 Originally Posted by Vee88 1. 2x / Cosx- Sinx = Cosx + Sinx 2.1 - Sin 2x / Sinx- Cosx = Sinx - Cosx 3.Sinx + Sinx /1 + Cosx + Cos2x = Tanx
Hi Vee88 and welcome to the forum. Tags determine, identities, values, variables 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 Vee88 Trigonometry 3 April 20th, 2018 06:38 AM Sparkleandpop Linear Algebra 1 September 29th, 2015 02:44 AM fixxit Algebra 4 September 10th, 2014 11:29 AM ka0ttic Computer Science 3 March 17th, 2014 04:08 AM dendimiiii Applied Math 1 February 12th, 2014 08:18 AM

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