SOLUTION: prove the identity cos theta sec theta/cot theta = tan theta

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Question 105991This question is from textbook Precalculus
: prove the identity

cos theta sec theta/cot theta = tan theta



This question is from textbook Precalculus

Found 2 solutions by edjones, chitra:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
cos theta sec theta/cot theta = tan theta
I will change theta to x for the sake of simplicity.
.
(cos(x)*1/cos(x))*sin(x)/cos(x)=sin(x)/cos(x)=tan(x)
Ed

Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
Here i'm representing theta as x since writing theta everytime would be a tedious task.

So the given problem can be written as:


%28%28Cos+x+Sec+x+%29%2FCot+x%29 = tan x

We know that Cos and Sec are reciprocal of each other. And also tan and cot are also reciprocate of each other. That is

Cos+x+=+%281%2FSec+x%29

And

+Tan+x+=+%281%2FCot+x%29


so using the above in the given expression, we get:


%28%28cosx+%2Asecx%29%2Fcotx%29


==> %28Cosx%281%2FCosx%29%29%2F%281%2Ftanx%29


The cos gets cancelled and we remain with %281%2F%281%2Ftan+x%29%29


so that is nothing but tan x

hence the solution.