Question

Make the indicated trigonometric substitution in the given algebraic expression and simplify . Assume 0 ≤ θ ≤ π/2 √1 + x² , x = sec θ

Answer 1

To make the indicated trigonometric substitution in the given algebraic expression and simplify, substitute x = sec θ and express √(1 + x²) in terms of θ.

Step-by-step explanation:

To make the indicated trigonometric substitution in the given algebraic expression and simplify, we substitute x = sec θ. This substitution allows us to express √(1 + x²) in terms of θ.

By substituting x = sec θ into √(1 + x²), we get √(1 + sec² θ).

Example: If θ = π/6, then x = sec(π/6) = 2.