SOLUTION: sec(x)=tan(x)csc(x)

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Question 739523: sec(x)=tan(x)csc(x)
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
sec(x)=tan(x)csc(x)
You will need to know 

This quotient identity:

#1. tan%28theta%29=sin%28theta%29%2Fcos%28theta%29

and these reciprocal identities 

#2. csc%28theta%29=1%2Fsin%28theta%29

#3. 1%2Fcos%28theta%29=sec%28theta%29

We will work ONLY with the right side:

sec(x) = tan(x)csc(x)

Use identity #1 to substitute sin%28x%29%2Fcos%28x%29 for tan(x).
Use identity #2 to substitute 1%2Fsin%28x%29 for csc(x).

sec(x) = expr%28sin%28x%29%2Fcos%28x%29%29%22%22%2A%22%22expr%281%2Fsin%28x%29%29

Cancel the sin(x)'s

sec(x) = expr%28cross%28sin%28x%29%29%2Fcos%28x%29%29%22%22%2A%22%22expr%281%2Fexpr%28cross%28sin%28x%29%29%29%29

That is equivalent to:

sec(x) = 1%2Fcos%28x%29

Now use identity #3 to substitute sec(x) for 1%2Fcos%28x%29

sec(x) = sec(x)

Edwin