SOLUTION: Make the trigonometric substitution x = a tan θ for −π/2 < θ < π/2 and a > 0. Simplify the resulting expression. x2/{{{sqrt(a^2 + x^2)}}} Please help! I do not know w

Algebra ->  Equations -> SOLUTION: Make the trigonometric substitution x = a tan θ for −π/2 < θ < π/2 and a > 0. Simplify the resulting expression. x2/{{{sqrt(a^2 + x^2)}}} Please help! I do not know w      Log On


   

Question 1159218: Make the trigonometric substitution
x = a tan θ for −π/2 < θ < π/2 and a > 0.
Simplify the resulting expression.
x2/sqrt%28a%5E2+%2B+x%5E2%29
Please help! I do not know what I am substituting nor do I know how to solve this problem.
Answer by MowMow(42) About Me  (Show Source):
You can put this solution on YOUR website!
x^2/SQRT(a^2 + a^2Tan^2θ)
x^2/SQRT(a^2(1+Tan^2θ)) = x^2/SQRT(a^2Sec^2(θ)) = a^2Tan^2θ /(a^2Sec^2θ)
= aTan^2θ/Secθ = aSin^2θ(Cosθ)/Cos^2θ) = aSin^2θ/Cosθ