Verify the identity.
cosine of x divided by quantity one plus sine of x plus quantity one plus sine of x divided by cosine of x equals two times secant of x.

For the answer to the question above,
cosx/(1+sinx) + (1+sinx)/cosx 
= (cosx * cosx + (1+sinx)(1+sinx)) / (cosx (1+sinx)) 
= (cos²x + sin²x + 2 sinx + 1) / (cosx (1+sinx)) 
= (1 + 2 sinx + 1) / (cosx (1+sinx)) 
= (2 + 2 sinx) / (cosx (1+sinx)) 
= 2 (1+sinx) / (cosx (1+sinx)) 
= 2/cosx 
= 2 secx
I hope my answer helped you. Have a nice day!

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