How would you prove:

(1-tan theta) squared= sec squared theta -2 tan theta

This isn't a bad one by comparison.

Exapnd out and look at it.

(1-tan{\theta})^{2}=1-2tan{\theta}+tan^{2}{\theta}

Now, what does 1+tan^{2}{\theta} equal?

(1-tan theta) squared = sec squared theta - 2 tan theta
1 + tan square theta - 2 tan theta
sec square theta - 2 tan theta
[since 1+tan square theta = sec square theta]

cot theta + (sin theta/1+cos theta)= csc theta

Could you avoid double posting please?

I already answered your question here (https://www.askmehelpdesk.com/high-school/how-would-you-prove-cot-theta-sin-theta-1-cos-theta-csc-theta-502213.html)