Hey, need some help with two questions (may be adding more to this thread later). I am finding these problems rather difficult, so an explanation of each step needed would be EXTREMELY HELPFUL!

1. $\displaystyle (secx - cosx)(cscx - sin x) = \frac{tanx}{1+tan^2x} $

My attempt:

LHS

= $\displaystyle (\frac{1}{cosx} - cosx)(\frac{1}{sinx} - sinx) $ *changed secx to 1/cosx, changed cscx to 1/sinx

= $\displaystyle (\frac{sin^2x + cos^2x}{cosx} - cosx)(\frac{sin^2x + cos^2x}{sinx} - sinx) $ *replaced "1" with pythagrean

This is where I am stuck as to what to do.

2. $\displaystyle sec^6x - tan^6x = 1 + 3tan^2x sec^2x $

My attempt:

LHS

= $\displaystyle (\frac{1}{cos^6x}) - (\frac{sin^6x}{cos^6x}) $ *changed tanx to sinx/cosx, changed secx into 1/cosx

= $\displaystyle (\frac {sin^2x + cos^2x} {cos^6x}) - (\frac{sin^6x}{cos^6x}) $ * Replaced "1" with pythagrean

Unknown what to do from here.

EDIT: Okay, I just read the rules. My apologies for all with the title involving "help" I should have been more specific. Unknown if possible to change title or not, I do not see a way right now.

What I did in the edit:

Showed my attempts and tried to explain what I was thinking for each step.

EDIT2: K, everything is in LaTeX! Took about 10 minutes extra, but WOW, looks a lot neater and easier to understand! Really glad I read the rules.