Triangles AOC and BOD are congruent by SAS. Therefore, and these lengths can be found using the . Because this is the unit circle, the coordinates of points A, B, and C are equal to cosine and sine of , – β, and β respectively. Write expressions for the lengths, set them equal, and square both sides of the equation. Simplifying the resulting expressions involving cosine and sine of , β, and – β requires using the identity. When simplified, the equation becomes cos( – β) = cos()cos(β) + sin()sin(
C
difference of their y-coordinatesSince triangles AOC and BOD are congruent, their corresponding sides have equal lengths. To write expressions for those lengths from the points’ coordinates, use the distance formula: for points (x₁, y₁) and (x₂, y₂), the distance is √((x₂ − x₁)² + (y₂ − y₁)²). Squaring the equal lengths then lets you simplify using the Pythagorean identity, but the method for finding the lengths is the distance formula.
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