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Establish the identity: tang fada+cot fada divided by sec fada csc fada =1

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2 Answers

Let x = fada
 
(tanx + cotx)/(secx cscx)
= tanx/(secx cscx) + cotx/(secx cscx)
= sin^2x + cos^2x, since tanx/(secx cscx) = sin^2x, cotx/(secx cscx) = cos^2x
= 1
Cailin,
 
I am assuming that "fada" is the strange name of some variable we would normally call "x" or theta or something.  But the math itself should be the same.
 
[tan(fada) + cot (fada)]/[sec(fada)*csc(fada)] 
 
First, let's consider the numerator all by itself
 
tan(fada) + cot(fada) = [sin(fada)/cos(fada)] + [cos(fada)/sin(fada)] = 1/[sin(fada)*cos(fada)]
 
Now consider the denominator all by itself:
 
csc(fada) = 1/[sin(fada)] and sec(fada) = 1/[cos(fada)]
 
so that sec(fada)*csc(fada) = 1/[sin(fada)*cos(fada)]
 
Thus, the numerator and denominator equal one another and when we divide one into the other, the answer is always 1 (which is what we were trying to show).