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hypotenuse ÷ adjacent
adjacent ÷ hypotenuse
opposite ÷ adjacent
hypotenuse ÷ opposite

try putting sec and cot in terms of trig properties i.e.) sin = opp/hyp and such

man you are all over the place today
solving equations, and now trig?! what kind of class is this?

\[\sec(x)=\frac{hyp}{adj}\]
\[\cot(x)=\frac{adj}{opp}\]
multiply and cancel

\[\frac{hyp}{adj}\times \frac{adj}{opp}=\frac{hyp}{opp}\]

also what @waterineyes said, but you are asked for the ratios
\[\csc(x)=\frac{hyp}{opp}\] too

\[cosec(x) = \frac{Hypotenuse}{Opposite}\]

I am bit slow in typing..

thankyou SOOOOO much!

Welcome dear..