Question

prove: (sin3x)(1+cot2x)=sinx

How?

Answer 1

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.

Answer 2

did you mean cos (2x)?

Answer 3

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

Answer 4

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

Answer 5

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