By definition of cosine and sine,
cos(θ) = x/r
sin(θ) = y/r
so that
cos²(θ) + sin²(θ) = (x/r)² + (y/r)²
… = x²/r² + y²/r²
… = (x² + y²)/r²
… = r²/r²
… = 1
To that end, I would say
• [blank1] = "Division property of equality"
That is, we divide both sides of an equation by the same number and equality still holds since r ≠ 0
• [blank2] = "Definition of cos"
• [blank3] = "cos²(θ) = x²/r²"
• [blank4] = "Defintion of sin"
• [blank5] = "sin²(θ) = y²/r²"
• [blank6] = "Simplify"
More specifically, x² + y² = r² is given, so
x²/r² + y²/r² = (x² + y²)/r² = r²/r² = 1