Question 588572: I need to prove this problem:
sec^2 t / tan t = (sec t)(csc t)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! tan(t) = sin(t) / cos(t)
sin(t) = 1/csc(t)
cos(t) = 1/sec(t)
by substitution, tan(t) = (1/csc(t)) / (1/sec(t))
this is equivalent to:
tan(t) = (1/csc(t))*sec(t) which is equivalent to:
tan(t) = sec(t)/csc(t)
your original equation is:
sec^2(t)/tan(t) = sec(t)*csc(t)
multiply both sides of this equation by tan(t) to get:
sec^2(t) = sec(t)*csc(t)*tan(t)
substitute sec(t)/csc(t) for tan(t) to get
sec^2(t) = sec(t)*csc(t)*sec(t)/csc(t)
the csc(t) in the numerator and denominator cancel out and you are left with:
sec^2(t) = sec(t)*sec(t)
since sec(t)*sec(t) is equal to sec^2(t), you are done.
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