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Sin(x)/Cos(x) + Cos(x)/1 + Sin(x) 

Guest Jun 12, 2015

Best Answer 

 #1
avatar+92781 
+10

I assume that you really mean this     

Sin(x)/Cos(x) + Cos(x)/(1 + Sin(x) )

 

$$\\\frac{Sin(x)}{Cos(x)} + \frac{Cos(x)}{1 + Sin(x) }\\\\
=\frac{Sin(x)}{Cos(x)} + \frac{Cos(x)(1-sin(x)) }{(1 + Sin(x))(1-sin(x)) }\\\\
=\frac{Sin(x)}{Cos(x)} + \frac{Cos(x)(1-sin(x)) }{(1-sin^2(x)) }\\\\
=\frac{Sin(x)}{Cos(x)} + \frac{Cos(x)(1-sin(x)) }{cos^2(x) }\\\\
=\frac{1}{Cos(x)}\\\\
=sec(x)$$

Melody  Jun 12, 2015
 #1
avatar+92781 
+10
Best Answer

I assume that you really mean this     

Sin(x)/Cos(x) + Cos(x)/(1 + Sin(x) )

 

$$\\\frac{Sin(x)}{Cos(x)} + \frac{Cos(x)}{1 + Sin(x) }\\\\
=\frac{Sin(x)}{Cos(x)} + \frac{Cos(x)(1-sin(x)) }{(1 + Sin(x))(1-sin(x)) }\\\\
=\frac{Sin(x)}{Cos(x)} + \frac{Cos(x)(1-sin(x)) }{(1-sin^2(x)) }\\\\
=\frac{Sin(x)}{Cos(x)} + \frac{Cos(x)(1-sin(x)) }{cos^2(x) }\\\\
=\frac{1}{Cos(x)}\\\\
=sec(x)$$

Melody  Jun 12, 2015

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