Question

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 D are equal to cosine and sine of α + β, α, and –β, respectively. Write expressions for the lengths and set them equal. Rewrite cos(-β) and sin(-β) using the identities before squaring both sides of the equation. Simplifying the resulting expressions involving cosine and sine of α, β, and α + β requires using the identity. When simplified, the equation becomes cos(α + β) = cos(α)cos(β) - sin(α)sin(β).

Answer 1

Based on the information given, it can be seen that Triangles AOC and BOD are congruent by SAS. Therefore, AC = BD.

What is a distance formula for a triangle?

It should be noted that the lengths can be found by using the distance formula. This is used to find the distance between two points. In this case, rewrite cos(-β) and sin(-β) using the even and odd identities before squaring both sides of the equation.

Lastly, simplifying the resulting expressions involving cosine and sine of α, β, and α + β requires using the Pythagoras identity.

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