SOLUTION: secant theata/tangent theata=cosecant theata

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Question 957165: secant theata/tangent theata=cosecant theata
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
For this I am going to replace theta with x.

%28sec%28x%29%29%2Ftan%28x%29=csc%28x%29

sec%28x%29 is the same as %281%29%2F%28cos%28x%29%29 and tan%28x%29 is the same as %28sin%28x%29%29%2F%28cos%28x%29%29.

Rewrite the equation.

%281%2Fcos%28x%29%29%2F%28sin%28x%29%2Fcos%28x%29%29

When you divide by a fraction, it is the same as multiplying by it's reciprocal.

%281%2Fcos%28x%29%29%2F%28sin%28x%29%2Fcos%28x%29%29
%281%2Fcos%28x%29%29%2A%28cos%28x%29%2Fsin%28x%29%29

The cos%28x%29 cancel and you are left with 1%2Fsin%28x%29 which is equivalent to csc%28x%29