SOLUTION: {{{tan^2(x)(1+cot^2(x)^"")=1/(1-sin^2(x))}}}

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Question 1154341: tan%5E2%28x%29%281%2Bcot%5E2%28x%29%5E%22%22%29=1%2F%281-sin%5E2%28x%29%29
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!

tan%5E2%28x%29%281%2Bcot%5E2%28x%29%5E%22%22%29=1%2F%281-sin%5E2%28x%29%29

Work with the left side:

tan%5E2%28x%29%281%2Bcot%5E2%28x%29%5E%22%22%29

Distribute:

tan%5E2%28x%29%2Btan%5E2%28x%29cot%5E2%28x%29%5E%22%22%29

Change the left side to sines and cosines:





Cancel:



sin%5E2%28x%29%2Fcos%5E2%28x%29%2B1

Get LCD:

sin%5E2%28x%29%2Fcos%5E2%28x%29%2Bcos%5E2%28x%29%2Fcos%5E2%28x%29

Combine numerators over LCD:

%28sin%5E2%28x%29%2Bcos%5E2%28x%29%29%2Fcos%5E2%28x%29

Use Pythagorean identity in numerator:

1%2Fcos%5E2%28x%29

Use Pythagorean identity in denominator:

1%2F%281-sin%5E2%28x%29%29

Edwin