Use fundamental identities to simplify the resulting expression.

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.

a2 − x2

x2

 

 

 

Answer 1

Working with just the discriminant:

 

a^{2 -} (a sinθ)²

a² - a² sin²Θ

a² (1 - sin²θ)

a² cos²θ  of which the square root is

 

a cosθ    now for the fraction

 

(a cosθ)/(a sinθ)

cosΘ/sinΘ

cotΘ