\(\bf \left[ 3sin(x)+3cos(x) \right]^2\impliedby \textit{using the binomial theorem}
\\\\\\
9sin^2(x)+18sin(x)cos(x)+9cos^2(x)
\\\\\\
9sin^2(x)+9cos^2(x)+18sin(x)cos(x)
\\\\\\
9[sin^2(x)+cos^2(x)]+18sin(x)cos(x)\\\\
-----------------------------\\\\
recall\to sin^2(\theta)+cos^2(\theta)=1\\\\
-----------------------------\\\\
\bf
9[1]+18sin(x)cos(x)\implies 9+18sin(x)cos(x)
\\\\\\
9[1+2sin(x)cos(x)]\\\\\)
\(\bf -----------------------------\\\\
recall\to sin(2\theta)=2sin(\theta)cos(\theta)\qquad thus\\\\
-----------------------------\\\\
9[1+sin(2x)]\)
