Question

How to simplify 3sin^2x + 3(1-sin^2x)

Answer 1

$\bf \textit{Pythagorean Identities}\\\\sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\[-0.35em]\rule{34em}{0.25pt}\\\\3sin^2(x)+3[1-sin^2(x)]\implies 3sin^2(x)+3cos^2(x)\\\\\\\stackrel{\textit{common factor}}{3[sin^2(x)+cos^2(x)]}\implies 3(1)\implies 3$