+0  
 
+1
159
2
avatar+5 

solve tan 2x = - cot (x + pi/3)

naincy  Mar 22, 2017
Sort: 

2+0 Answers

 #1
avatar+89762 
0

I have tried to post an answer but the site froze up and I lost it all.

Here is the short version

 

solve tan 2x = - cot (x + pi/3)

 

I solved by graphing.

 

Herer is the full graph

https://www.desmos.com/calculator/mblxlza8ms

 

From the graph it appears the answer is        \(x=n\pi+\frac{5\pi}{6}\qquad n \in Z\)

 

In my last (lost) answer I substituted this answer in to check it was correct and it was exactly so.

 

If you want to ask questions by all means do so :)

 

 

Here is the pic:

Melody  Mar 22, 2017
edited by Melody  Mar 22, 2017
 #2
avatar
+1

Don't know whether or not this is the long version, but Melody hasn't posted it so I will

\(\displaystyle \tan2x = -\cot(x+\pi/3),\\\frac{\sin2x}{\cos2x}=-\frac{\cos(x+\pi/3)}{\sin(x+\pi/3)},\\\sin2x\sin(x+\pi/3)=-\cos2x\cos(x+\pi/3),\\ \cos2x\cos(x+\pi/3)+\sin2x\sin(x+\pi/3)=0,\\\cos[2x-(x+\pi/3)]=0,\\\cos(x-\pi/3)=0,\\x-\pi/3=(2n+1)\pi/2=n\pi+\pi/2,\;\;n=0,\pm1,\pm2,\dots\\x=n\pi+5\pi/6,\;\;n=0,\pm1,\pm2,\dots\)

Guest Mar 23, 2017

8 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details