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(cosx / sinx) + (2sinx / cosx) + (sin^3x / cos^3x) How to simplify the expression with the LCM?

 Apr 2, 2017
 #1
avatar+130491 
0

The LCM  is sinx*cos^3x....so we have

 

cos(x) cos^3 (x) / [ sin (x) * cos^3 (x)] +

 

[2 sinx * sin x * cos^2 (x)] / [sin (x)cos^3 (x)] +

 

[ sin (x) sin^3(x)] / [ sin(x) cos^3 (x) ]  =

 

 

[cos^4 (x) + 2 sin (x) cos^3(x) + sin^4 (x)] / [ sin (x)cos^3(x) ] =

 

[cos^4 (x) + 2 sin (x) cos(x) * cos^2(x) + sin^4 (x)] / [ sin (x)cos^3(x) ]  =

 

[ cos^4 (x) + sin(2x)*cos^2(x) + sin^4(x) ]  / [ sin(x)cos^3(x) ]

 

 

cool cool cool

 Apr 2, 2017
 #2
avatar+26397 
+2

(cosx / sinx) + (2sinx / cosx) + (sin^3x / cos^3x)

How to simplify the expression with the LCM?

 

cos(x)sin(x)+2sin(x)cos(x)+sin3(x)cos3(x)=cos(x)sin(x)cos3(x)cos3(x)+2sin(x)cos(x)sin(x)cos2(x)sin(x)cos2(x)+sin3(x)cos3(x)sin(x)sin(x)=cos(x)cos3(x)+2sin(x)sin(x)cos2(x)+sin3(x)sin(x)sin(x)cos3(x)=cos4(x)+2sin2(x)cos2(x)+sin4(x)sin(x)cos3(x)=sin4(x)+2sin2(x)cos2(x)+cos4(x)sin(x)cos3(x)=(sin2(x)+cos2(x))2sin(x)cos3(x)|sin2(x)+cos2(x)=1=12sin(x)cos3(x)=1sin(x)cos3(x)

 

laugh

 Apr 3, 2017

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