TRIG SUBSTITUTION

Question

Make the trigonometric substitution
x = a sin θ for −π/2 < θ < π/2 and a > 0.
Use fundamental identities to simplify the resulting expression.

√(a^2 − x^2)
x^2
PLEASE SHOW HOW TO DO THIS PROBLEM

Answer 1

x=asinθ

√(a^2-x^2)

x^2=(asinθ)^2

x^2=a^2(sin^2(θ))

substitute

√(a^2-[a^2(sin^2(θ))])

factor

√[a^2(1-sin^2(θ)]

sin^2(θ)+cos^2(θ)=1

cos^2(θ)=1-sin^2(θ)

substitute again

√(a^2)(cos^2(θ))

a cos(θ) is the answer after simplifying the radicand