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

 Apr 1, 2016
 #1
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(sin x)/(1 + cos x) + (1+ cos x)/(sin x) = 2 csc x

 

The first thing that always strikes me here, Shades, is to get a common denominator on the left, and then see if something "falls out."

 

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

 

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

 

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

 

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

 

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

 

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

 

2 / sinx  =

 

2 (1/sinx)  =

 

2 (csc x)

 

 

 

cool cool cool

 Apr 1, 2016

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