Proving trig Identities: Cos(x)/(1 - sin(x)) = sec(x)+tan(x)

[davidegli_101]

Hey I have this question that I can't figure out.

(Cos (x))/(1 - sin(x)) = sec(x) + tan(x)

Thanks!

 

[Mrspi]

Hey I have this question that I can't figure out.

(Cos (x))/(1 - sin(x)) = sec(x) + tan(x)

Thanks!

Have you thought about multiplying numerator and denominator of the left side by (1 + sin x)?

cos x * (1 + sin x)
--------------------
(1 - sin x)(1 + sin x)

cos x * (1 + sin x)
-------------------
1 - sin^2 x

Now...what is 1 - sin^2 x (from the Pythagorean identities)?

Make the substitution...and reduce the fraction.

Then, see where that takes you.