## anonymous 5 years ago prove: (sin3x)(1+cot2x)=sinx How?

1. anonymous

Well, looking at the graph of (sin 3x)(1+cot 2x) it doesn't look much like sin x. So I'm guessing that's gonna be a hard one to prove.

2. anonymous

did you mean cos (2x)?

3. anonymous

prove (sin^3x)(1+cot^2x)=sinx

4. anonymous

Do you mean? $(sin\ x)^3[1+(cot\ x)^2] = sin\ x$

5. anonymous

$(sin\ x)^3[1+(cot\ x)^2]$ $=(sin\ x)^3 + (sin\ x)^3(cot\ x)^2$ $= (sin\ x)[(sin\ x)^2 + \frac{(sin\ x)^2(cos\ x)^2}{(sin\ x)^2}]$ $= (sin\ x)[(sin\ x)^2 + (cos\ x)^2]$ $= (sin\ x)(1)$ $= sin\ x$