20 ! how to prove that sec(theta)/tan(theta)=csc(

when proving trigonometric identities, each side must be treated separately. we must show that both sides can attain the same form.focusing on the left-hand side because it looks more  complicated (easier to simplify something complex than it is to make something more complex):     one strategy is to turn everything in terms of sine and cosine.since we have these identities and  , we can do    note that this is just division.    dividing by a fraction is the same as multiplying by the reciprocal. then the cosines cancel out.    by definition,  so