SOLUTION: I'm having a huge problem proving this Trig Identity; (secx)/(sinx) - (sinx)/(cosx) = cotx Please help

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Question 752542: I'm having a huge problem proving this Trig Identity;
(secx)/(sinx) - (sinx)/(cosx) = cotx
Please help
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28sec%28x%29%2Fsin%28x%29%29+-+%28sin%28x%29%2Fcos%28x%29%29+=+cot%28x%29

.....since 1%2F%28sinx%29=csc%28x%29 and %28sin%28x%29%29%2F%28cos%28x%29%29+=+tan%28x%29, we will have

sec%28x%29csc%28x%29+-+tan%28x%29+=+cotx........since sec%28x%29+=+1+%2F+cos%28x%29 => cos%28x%29+=+1+%2F+sec%28x%29, then tan%28x%29=sec%28x%29sin%28x%29

sec%28x%29csc%28x%29+-+sec%28x%29sin%28x%29+=+cot%28x%29

sec%28x%29%28csc%28x%29+-+sin%28x%29%29+=+cot%28x%29

sec%28x%29%28csc%28x%29+-+sin%28x%29%29+=+cot%28x%29........since csc%28x%29+-+sin%28x%29=cos%28x%29cot%28x%29

sec%28x%29cos%28x%29cot%28x%29+=+cot%28x%29........again sec%28x%29+=+1+%2F+cos%28x%29

%281+%2F+cos%28x%29%29cos%28x%29cot%28x%29+=+cot%28x%29

%281+%2F+cross%28cos%28x%29%29%29cross%28cos%28x%29%29cot%28x%29+=+cot%28x%29

cot%28x%29+=+cot%28x%29

Answer by Edwin McCravy(20060) About Me  (Show Source):