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

Question 1159218: Make the trigonometric substitution
x = a tan θ for −π/2 < θ < π/2 and a > 0.
Simplify the resulting expression.
x2/
Please help! I do not know what I am substituting nor do I know how to solve this problem.
Answer by MowMow(42) (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
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