Verify that: (1 + sinx)/(cosx) = (cosx)/(1 - sinx)

Please show work.

Take (1+sinx)/cosx and multiply numerator and denominator by (1-sinx) to get

(1-sinx)(1+sinx)/(cosx)(1-sinx)
= (1-sin^2x)/cosx(1-sinx)

Apply 1-sin^2x = cos^2x

...= cos^2x/cosx(1-sinx)

cancel cosx
... = cosx/(1-sinx) = RHS

Let us define f(x) Tge difference between the two terms. We are going to prove that f(x) =0 for all values of x .
Remember that cos^2 x + sin^2 x =1 for all x.
f(x)=(1+sinx)/cosx -cosx/(1-sinx)=1-sin^2x-cos^2x/cosx*(1-s…
The numerator 1-(sin^2x+cos^2x)=1-1=0 which proves that f(x)=0 and thus the two expressions are equal.