Question

Simplify the expression (tan x)(1 - sin² x)1/2. Show your work. (10 points)

Answer 1

`\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \\\\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\ -------------------------------\\\\ \cfrac{tan(x)[1-sin^2(x)]}{2}\implies \cfrac{(sin(x))/(cos(x))\cdot cos^2(x)}{2}\implies \boxed{\cfrac{sin(x)cos(x)}{2}}`