Trgonometric Substitution

Question 1

What is the substitution for sqrt(a^2-x^2)

Answer 1

X=a sin x

Identity 1-sin^2x = cos^2x

Question 2

What is the substitution for expression sqrt(a^2+x^2)

Answer 2

X=a tan x

Identity 1+tan^2x=sec^2x

Question 3

What is the substitution for sqrt(x^2-a^2)

Answer 3

X=a sec x

Sec^2x-1=tan^2x