I am having issues with those one. I do not know how to solve.

## 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).