+0  
 
0
264
2
avatar+466 

sin x/1 + cos x + 1 + cos x/sin x = 2 csc x

Show that the left side equals the right side. frown angry

Shades  Feb 15, 2016

Best Answer 

 #1
avatar+78719 
+5

I think this is supposed to be :

 

sin x / (1 + cos x) + (1 + cos x)/sin x = 2 csc x    

 

get a common denominator on the left   = sinx (1 + cos x)

 

[ sinx (sinx)   + ( 1 + cosx)^2 ] /  [ sinx (1 + cosx)]

 

[sin^2x + 1 + 2cosx + cos^2x] / [ sinx(1 + cosx)]

 

[sin^2x + cos^2x + 1 + 2cosx] / [ sinx(1 + cosx)]  

       

{remember : sin^2x + cos^2x  = 1}

 

[ 1 + 1 + 2 cosx] / [sinx (1 + cosx)]

 

[2 + 2cos x]  /  [ sinx (1 + cos x) ]        factor out 2 on top

 

2(1 + cosx)  / [sinx ( 1 + cosx)]         "cancel "   the (1 + cos x) on top/bottom

 

2 / sinx  =

 

2 (1 / sinx)  =

 

2csc x         and this =  the right hand side

 

 

 

cool cool cool

CPhill  Feb 15, 2016
edited by CPhill  Feb 15, 2016
Sort: 

2+0 Answers

 #1
avatar+78719 
+5
Best Answer

I think this is supposed to be :

 

sin x / (1 + cos x) + (1 + cos x)/sin x = 2 csc x    

 

get a common denominator on the left   = sinx (1 + cos x)

 

[ sinx (sinx)   + ( 1 + cosx)^2 ] /  [ sinx (1 + cosx)]

 

[sin^2x + 1 + 2cosx + cos^2x] / [ sinx(1 + cosx)]

 

[sin^2x + cos^2x + 1 + 2cosx] / [ sinx(1 + cosx)]  

       

{remember : sin^2x + cos^2x  = 1}

 

[ 1 + 1 + 2 cosx] / [sinx (1 + cosx)]

 

[2 + 2cos x]  /  [ sinx (1 + cos x) ]        factor out 2 on top

 

2(1 + cosx)  / [sinx ( 1 + cosx)]         "cancel "   the (1 + cos x) on top/bottom

 

2 / sinx  =

 

2 (1 / sinx)  =

 

2csc x         and this =  the right hand side

 

 

 

cool cool cool

CPhill  Feb 15, 2016
edited by CPhill  Feb 15, 2016
 #2
avatar+466 
+5

Yes, thank you very much! I had a factoring question that I wrote, but it didn't appear on the forum, so if you could answer this one too, I would greatly appreciate it: http://web2.0calc.com/questions/factoring_2753     cool

Shades  Feb 15, 2016

4 Online Users

avatar
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