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Various trigonometric identities and formulas, including pythagorean identities, double angle identities, half angle identities, tangent formulas, addition and subtraction formulas, and product to sum formulas.
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Pythagorean Identities sin^2 x + cos^2 x = 1 (1) 1 + cot^2 x = csc^2 x (2) tan^2 x + 1 = sec^2 x (3) Double Angle Identities sin(2x) = 2sin xcos x (4) cos(2x) = cos^2 x - sin^2 x (5) cos(2x) = 2cos^2 x – 1 (6) cos(2x) = 1 – 2sin^2 x (7) Half Angle identities cos^2 x = 1 2 (1+cos(2x)) (8) sin^2 x = 1 2 (1 – cos(2x)) (9) Tangent formulas tan x = sin 𝑥 cos 𝑥
𝑑 𝑑𝑥 tan x = sec^2 x (11)
Addition and Subtraction formulas sin(A+B) = sin Acos B + cos Asin B (12) sin(A – B) = sin Acos B – cos Asin B (13) cos(A+B) = cos Acos B – sin Asin B (14) cos(A – B) = cos Acos B + sin Asin B (15) Product to Sum formulas sin A sin B = 1 2 cos(A – B) – 1 2 cos(A + B) (16) cos A cos B = 1 2 cos(A – B) + 1 2 cos(A + B) (17) sin A cos B = 1 2 sin(A + B) + 1 2 sin(A - B) (18) cos A sin B = 1 2 sin(A + B) – 1 2 sin(A - B) (19)
