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

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 April 21st, 2018, 07:39 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 02:36 PM.
 April 21st, 2018, 08:10 AM #2 Senior Member   Joined: Oct 2009 Posts: 608 Thanks: 186 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 09:28 AM.
 April 21st, 2018, 11:00 AM #3 Global Moderator   Joined: Dec 2006 Posts: 19,865 Thanks: 1833 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, 02:38 PM   #4
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 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.

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