Establishing trig identities.?

I do not need the whole problem worked out for me and explained to me, just a piece. MyMathLab works a lot of it out and gives the answer, but it is not being very specific, and I don't understand one part of this problem.

The part I do not understand:

(2 secant theta tangent theta) = (2 sine theta) / (cosine^2 theta)

How do I get from the left side of the equation to the right?

If it helps, the original problem was:

(1-sine theta) / (1+sine theta) = (secant theta - tangent theta)^2

Like I said, the part that I am confused with is only a small piece of this puzzle. I understand MML for everything but the piece I am having a hard time with, so you do not have to waste your time on working out the whole thing for me. In fact, it will probably be less confusing if you can *only* tell me the answers to the small piece I am having trouble with.

Thanks!

Relevance
• Casey
Lv 5
8 years ago

It is actually quite simple.

sec(theta) = 1/cos(theta)

tan(theta) = sin(theta)/cos(theta)

multiply those together:

[sin(theta)/(cos^2(theta)]*2

There you go. Hope that helps.

• 8 years ago

express everything in terms of sine and cosine (use trig identities)