SOLUTION: Hi, I'm stumped on this Trigonometry Proof, {{{ (cos(x)/sec(x)) - (cot(x)/tan(x)) = (-cos^2(x))(cot^2(x)) }}} I've tried switching the denominators to their opposites, ie: {{

Question 693043: Hi, I'm stumped on this Trigonometry Proof,

I've tried switching the denominators to their opposites, ie: to . I've tried to substitute in some identities after that step too, but I can't get it.
Thanks!

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

You had a good idea with replacing the denominators. Replacing sec(x) with 1/cos(x) and tan(x) with 1/cot(x) we end up with:

Since the right side is a product we want to be able to write the right side as a product, too. So we are looking to factor the left side. While the left side is a difference of squares, factoring it that way does not (as far as I can tell) get us closer to the end of the proof. Instead we should know that . Looking at this way we can see that
If we're really cleaver we would factor out since that is a factor of the right side:

We can replace the fraction with :

From one of the Pythagorean identities :

which simplifies to:

And we are finished.
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