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

[physicsdreams]

Homework Statement

Prove.

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

Homework Equations

Trig Identities

The Attempt at a Solution

I decided to try and prove the identity by manipulating the function on the right side.

I multiplied both the numerator and denominator by (1+cos) and got
(sin(x)(1+cos))/(1-cos^2)
→(sin(x)(1+cos))/(sin^2)
→(1+cos)/(sin)
→(csc)+(1/tan)

I'm stuck after this point.
All help is much appreciated.
Thank you.

 

[Joffan]

You're so close...

You have (1+cos)/(sin)

divide numerator and denominator by cos...

 

[physicsdreams]

You're so close...

You have (1+cos)/(sin)

divide numerator and denominator by cos...

Thank you very much!

I would never have thought of multiplying by (1/cos) because it seemed so...random, yet it works.

Do you have any tips on how to see things like that?