Math
Sum and difference formulas.
Definition
Trigonometric identities that express sin(A ± B), cos(A ± B), and tan(A ± B) in terms of sin, cos, and tan of A and B individually. They are essential for finding exact values of trig functions at non-standard angles.
Examples
Real-world.
- 1 sin(75°) = sin(45° + 30°) = sin45·cos30 + cos45·sin30 = (√6 + √2)/4
- 2 cos(15°) = cos(45° − 30°) = cos45·cos30 + sin45·sin30 = (√6 + √2)/4
Key Fact
sin(A ± B) = sinA·cosB ± cosA·sinB; cos(A ± B) = cosA·cosB ∓ sinA·sinB
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