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anderson17 · May 3, 2010, 03:41 PM

How do prove this to be true?

(secθ/sinθ) - (sinθ/cosθ) = cotθ

ArcSine · May 4, 2010, 04:51 AM

Let's fiddle with the left-hand side. Re-write the first term as

$\frac{1}{sin(x)cos(x)}$

Multiply the second term by "1", in the form of $\frac{sin(x)}{sin(x)}$ and it becomes $\frac{sin^2(x)}{sin(x)cos(x)}$

Now both terms of the LHS have the same denominator, and can therefore be combined. Next, apply the Pythagorean Identity to the resulting numerator, and take it from there...