Question

let x=2sin(theta), -pi/2 < theta < pi/2. Simplify the expression

x/square root of 4-x^2

Answer 1

make the replacement just like you are asked
write
\[\frac{2\sin(\theta)}{\sqrt{4-(2\sin(\theta))^2}}\]

Answer 2

then the denominator can be manipulated as follows
\[\sqrt{4-(2\sin(\theta))^2}=\sqrt{4-4\sin^2(\theta)}\]
\[=\sqrt{4(1-\sin^2(\theta))}=\sqrt{4\cos^2(\theta)}=2\cos(\theta)\]