Make the indicated trigonometric substitution in the given algebraic expression and simplify (see Example 7). Assume that 0 < θ < π/2. x / sqrt(1 − x^2) , x = sin(θ)

Answer 1

This is then (sinx)/(1-sin^2x). 1-sin^2 x = cos^2 x so this simplifies to

(sinx)/(cos^2 x) = (sinx)(cosx) x 1/cos x= (tan x )(sec x)