Trig Identity Simplification of (cot(x)+tan(x))/tan(x)sec(x)

[BigNate]

Hello Everyone,

I cannot figure out the trig identities that would allow me to simplify this. The question is:

Which of the following is equal to (cot(x)+tan(x))/tan(x)sec(x)

...with the answer being cos(x)/sin^2(x)

Can someone please explain this to me?

 

[tkhunny]

tan(x) = sin(x)/cos(x)

cot(x) = cos(x)/sin(x)

Rule of Thumb: When in doubt, change everything to sine and cosine.