If x = 9tanθ, use trigonometric substitution to write square root 81 + x^2 as a trigonometric function of θ, where -pi/2 < θ < pi/2

Answer 1

√(81+x^2)
= √(81+81tan^2θ)
= √(81(1+tan^2θ))
= √(81sec^2θ)
= 9secθ

Looks like you need to brush up on your basic trig identities.