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avatar+41 

Hi.

 

Thank you so much in advance.

I need help proving

 \(csc(x)/(cot(x)+tan(x)) = cos(x)\)

 Aug 30, 2017
 #1
avatar+100529 
+2

 

csc x / [ cot x + tanx ]  =   write in terms of sine and cosine

 

[ 1 / sin x] / [( cos x / sinx) + (sin x / cos x) ]      get a common denominator on the bottom 

 

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

 

 

 1                               [ cos^2 x +  sin^2 x ]

___         ÷               ___________________       =

sin x                              sin x cosx 

 

 

  1                                    sin x cos x

___          X               ___________________   =        swap numerators

sin x                             [ cos^2 x +  sin^2 x ]

 

 

 

 sin x cos x        X           1

_________                  ____     =

  sin x                              1 

 

 

cos x

 

 

cool cool cool

 Aug 30, 2017

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