Advanced trigonometric identities
The sum and difference formulas let you find the sine, cosine, or tangent of an angle like 15 degrees or 75 degrees by breaking it into two angles you already know, such as 45 minus 30. For example, sin(A + B) = sin A cos B + cos A sin B, and cos(A + B) = cos A cos B - sin A sin B; from these you can also derive double-angle formulas like sin(2A) = 2 sin A cos A by setting B equal to A, so sin(2 x 30 degrees) = 2 sin(30) cos(30) = 2(0.5)(0.866) = 0.866, matching the known value of sin(60 degrees).
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