Question

Rewrite with only sin x and cos x.

sin 3x

Answer 1

`\bf \textit{triple angle identities}\\\\ sin(3\theta )=3sin(\theta )-4sin^3(\theta )\\\\ -------------------------------`


`\bf \begin{array}{llll} 3sin(\theta )&-2sin^3(\theta )&-2sin^3(\theta )\\\\ &-2\underline{sin^2(\theta )} sin(\theta )\\\\ &-2[\underline{1-cos^2(\theta )}]sin(\theta )\\\\ &[-2+2cos^2(\theta )]sin(\theta )\\\\ &-2sin(\theta )+2cos^2(\theta )sin(\theta ) \end{array} \\\\\\ 3sin(\theta )\boxed{-2sin(\theta )+2cos^2(\theta )sin(\theta )}-2sin^3(\theta ) \\\\\\ sin(\theta )+2cos^2(\theta )sin(\theta )-2sin^3(\theta ) \\\\\\ 2cos^2(\theta )sin(\theta )+sin(\theta )-2sin^3(\theta )`