Question

Simplify the expression: Sqrt(16 − x^2)

as much as possible after substituting "4 sin x" for x.

Answer 1

`\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\ -------------------------------\\\\ √(16-x^2)\implies √(16-[4sin(x)]^2)\implies √(16-[4^2sin^2(x)]) \\\\\\ √(16-16sin^2(x))\implies √(16[1-sin^2(x)])\implies √(16cos^2(x)) \\\\\\ √(4^2cos^2(x))\implies √([4cos(x)]^2)\implies 4cos(x)`