Use fundamental identities to simplify the resulting expression.

Question

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

 

b2 + x2

 

Answer 1

Working with just the discriminant:

 

b² + (b tanΘ)²

b² + b² tan²Θ

b² (1 + tan²Θ)

b² sec²θ        of which the square root is

b secθ