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\(\frac{1+sin(x)}{cos(x)}+\frac{cos(x)}{1+sin(x)}=\frac{2}{cos(x)}\) 

Well here is my steps: 

\(\frac{(1+sin^2(x))+cos^2(x)}{cos(x)(1+sin(x))}\)

 

 

\(\frac{2+2sin(x)}{cos(x)(1+sin(x))}\)

What to do from here?

 Jan 30, 2020
 #1
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On the left-hand side, when you multiplied [ 1 + sin(x) ]  times another [ 1 + sin(x) ],

you should get:     [ 1 + sin(x) ]2  =  1 + 2sin(x) + sin2(x)

 

Then continue ...

 Jan 30, 2020
 #2
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Hello geno,

I continued this step but didn't write it 

I.e. here it is:

\(\frac{1+sin^2(x)+2sin(x)+cos^2(x)}{cos(x)(1+sin(x))}\) 

\(sin^2(x)+cos^2(x)=1\)

Thus we have:

\(1+1+2sin(2)/cos(x)(1+sin(x))\)

Which is 

\(\frac{2+2sin(x)}{cos(x)(1+sin(x))}\) So the required is this should be simplified to be 2/cos(x)

Guest Jan 30, 2020
 #3
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nvm solved it, just factor 2 out of the numerator and 1+sin(x) cancels left with 2/cos(x)

Guest Jan 31, 2020

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