State whether or not the equation is an identity. Prove your statement.

Question

sin(x)/cos(x)+ cos(x)/1+sin(x)=sec(x)

Answer 1

I think you meant
sin(x)/cos(x)+ cos(x)/(1+sin(x))=sec(x)

LS = (sinx(1+sinx) + sinxcosx)/(cosx(1+sinx))
= (sinx + sin^2x + cos^2x)/(cosx(1+sinx))
= (sinx + 1)/(cosx(1+sinx))
= 1/cosx
= sec x
= RS