Answer:
The answer is a² .
Step-by-step explanation:
You have to substitute x and y into the expression :
[tex]let \: x = a \cos(θ) \\ let \: y = a \sin( θ)[/tex]
[tex] {x}^{2} + {y}^{2} = {(a \cosθ )}^{2} + {(a \sinθ) }^{2} [/tex]
[tex] {x}^{2} + {y}^{2} = {a}^{2}( {cos}^{2}θ) + {a}^{2} ({sin}^{2}θ)[/tex]
Next, you have to apply Basic Trigonometric Identity :
[tex] {sin}^{2} θ + {cos}^{2} θ = 1[/tex]
[tex] {x}^{2} + {y}^{2} = {a}^{2} ( {cos}^{2} θ + {sin}^{2} θ)[/tex]
[tex] {x}^{2} + {y}^{2} = {a}^{2} (1)[/tex]
[tex] {x}^{2} + {y}^{2} = { a}^{2} [/tex]
