Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume that ( √(x^2-36) )/(x) 0 ≤ θ < π/2. x=6secФ

Question

Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume that  
`( √(x^2-36) )/(x)`     0 ≤ θ < π/2.   

x=6secФ

Answer 1

After substituting:

`(√(36sec^2 \theta - 36))/(6 sec \theta)`
Factor out the 36, allowing the 6's to cancel

`( √(sec^2 \theta - 1))/(sec \theta)`
Use trig identity:
sec^2 - 1 = tan^2

`(√(tan^2 \theta))/(sec \theta) = (tan \theta)/(sec \theta) = sin \theta`