Question

how do I simplify this equation?
sinx(cscx-cotxcosx)

Answer 1

I usually just change everything to terms of sine and cosine

\[\large sin(x)(\frac{1}{sin(x)} - \frac{cos(x)}{sin(x)}cos(x))\]

Does this help at all?

Answer 2

I did that already but now what?

Answer 3

If you distribute that sin(x) into the parenthesis...this simplifies quite a bit :)

Answer 4

SO then (sinx/sinx-sinx(cosx/sinx)(cosx)) Then you can take out the sinx/sinx
so (cosx/sinx)(cosx) is what you have left over, am I right?

Answer 5

Not quite...remember that doesnt just go away :)

\[\large sin(x)(\frac{1}{sin(x)} - \frac{cos(x)}{sin(x)}cos(x))\]

Becomes \[\large \frac{sin(x)}{sin(x)} - \frac{sin(x)cos(x)}{sin(x)}cos(x)\]

So notice

\[\large \frac{\cancel{sin(x)}}{\cancel{sin(x)}} - \frac{\cancel{sin(x)}cos(x)}{\cancel{sin(x)}}cos(x)\]

Leaving us with

\[\large 1 - cos^2(x)\]

Make sense so far?

Answer 6

Yes and 1-cos^2x=sin^2x

Answer 7

Perfect :)

Answer 8

sweet thanks