How to solve for delta using trig functions? i.e. cosine sine tangent secant Thank you

I'm not sure what delta you're referring to. Could you please elaborate some for us. What is it you're trying to do with the trig funtions?

the problem is..

limit sec theda - 1/ theda sec theda
as theda approaches 0

find the limit

Ok, now I think I understand what you mean. We have:
"the problem is..

limit sec theda - 1/ theda sec theda
as theda approaches 0

find the limit"
This is the same as
limit theta->0 of (1/cos - 1)*cos/theta or,
limit theta->0 of (1-cos)/theta
You should have some limit theorems that justify the steps I did. It's just algebraic manipulation here.
Now evaluate the limit. You should have a result for this problem in your text. It's a very common one like sin/ theta.

x

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