Question

Perform the multiplication and use the fundamental identities to simplify.
(3sinx+3cosx)^2

Answer 1

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

$\bf -----------------------------\\\\ recall\to sin(2\theta)=2sin(\theta)cos(\theta)\qquad thus\\\\ -----------------------------\\\\ 9[1+sin(2x)]$