Question

Use trigonometric substitution to write the algebraic expression as a trigonometric function of θ, where 0 < θ <π/2.

√(100) - 4x^(2), x = 5cos(θ)

Answer 1

√(100) - 4x^(2), x = 5cos(θ),

case 1
perhaps it is √(100)² - 4x^(2), x = 5cos(θ)
because if so, √(100)²=100
√(100)² - 4x^(2) = 100- 100cos²(θ) = 100( 1 - cos²(θ))= 100sin²(θ), and
0 < θ <π/2.

case2
if it is true that √(100) - 4x^(2), the possible equality is √(100) - 100cos²(θ)