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)

√ (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)