Question

How do I simplify this?

`√(16-16sin^2x)`

Answer 1

`\textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] ~\dotfill\\\\ √(16 - 16sin^2(x))\implies √(16(~1-sin^2(x)~)) \implies √(4^2(~1-sin^2(x)~)) \\\\\\ √(4^2 (~cos^2(x)~))\implies √(4^2 (~cos(x)~)^2)\implies 4cos(x)`