Recall the definitions of the trig. functions:

    sint = y/r___________csct = r/y
    cost = x/r___________sect = r/x
    tant = y/x___________cott = x/y

Now the "proofs"

__csct
= r/y
= 1/(y/r)
= 1/sint
__sect
= r/x
= 1/(x/r)
= 1/cost
__tant
= y/x
= (y/r)/(x/r) dividing both top_____
= (y/r)/(x/r) and bottom by r
= sint /cost
__cott
= x/y
= 1/(y/x)
= 1/tant
= 1/(sint /cost)
= cost /sint

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