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

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?

Guest Jan 30, 2020

#1**0 **

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) + sin^{2}(x)

Then continue ...

geno3141 Jan 30, 2020

#2**0 **

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