+0  
 
0
293
2
avatar

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

Guest Apr 2, 2017
 #1
avatar+87309 
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

CPhill  Apr 2, 2017
 #2
avatar+19653 
+2

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

How to simplify the expression with the LCM?

 

\(\begin{array}{|rcll|} \hline && \frac{\cos(x)}{\sin(x)} + \frac{2\sin(x) }{ \cos(x) } + \frac{ \sin^3(x) } { \cos^3(x) } \\ &=& \frac{\cos(x)}{\sin(x)}\cdot \frac{\cos^3(x)}{\cos^3(x)} + \frac{2\sin(x) }{ \cos(x) } \cdot \frac{\sin(x)\cos^2(x)}{\sin(x)\cos^2(x)} + \frac{ \sin^3(x) } { \cos^3(x) }\cdot \frac{ \sin(x) } { \sin(x) } \\ &=& \frac{\cos(x)\cos^3(x)+ 2\sin(x)\sin(x)\cos^2(x) + \sin^3(x)\sin(x) } {\sin(x)\cos^3(x) } \\ &=& \frac{\cos^4(x)+ 2\sin^2(x)\cos^2(x) + \sin^4(x) } {\sin(x)\cos^3(x) } \\ &=& \frac{\sin^4(x)+2\sin^2(x)\cos^2(x)+\cos^4(x) } {\sin(x)\cos^3(x) } \\ &=& \frac{\Big( \sin^2(x)+\cos^2(x) \Big)^2 } {\sin(x)\cos^3(x) } \quad & | \quad \sin^2(x)+\cos^2(x) = 1 \\ &=& \frac{ 1^2 } {\sin(x)\cos^3(x) } \\ &=& \frac{ 1 } {\sin(x)\cos^3(x) } \\ \hline \end{array} \)

 

laugh

heureka  Apr 3, 2017

9 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.