Here are all the trigonometric formulas:

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  1. Sine formula: sin A = opposite/hypotenuse
  2. Cosine formula: cos A = adjacent/hypotenuse
  3. Tangent formula: tan A = opposite/adjacent
  4. Pythagorean theorem: hypotenuse^2 = opposite^2 + adjacent^2
  5. Reciprocal identities: csc A = hypotenuse/opposite, sec A = hypotenuse/adjacent, cot A = adjacent/opposite
  6. Quotient identities: tan A = sin A / cos A, cot A = cos A / sin A
  7. Even/odd identities: sin (-A) = -sin A, cos (-A) = cos A
  8. Sum and difference formulas: sin (A + B) = sin A cos B + cos A sin B, cos (A + B) = cos A cos B - sin A sin B, tan (A + B) = (tan A + tan B) / (1 - tan A tan B)
  9. Double angle formulas: sin 2A = 2 sin A cos A, cos 2A = cos^2 A - sin^2 A, tan 2A = (2 tan A) / (1 - tan^2 A)
  10. Half angle formulas: sin (A/2) = ± √((1 - cos A) / 2), cos (A/2) = ± √((1 + cos A) / 2), tan (A/2) = ± √((1 - cos A) / (1 + cos A))
  11. Product to sum identities: sin A sin B = (1/2) [cos(A-B) - cos(A+B)], cos A cos B = (1/2) [cos(A-B) + cos(A+B)], sin A cos B = (1/2) [sin(A+B) + sin(A-B)]
  12. Sum to product identities: sin A + sin B = 2 sin[(A+B)/2] cos[(A-B)/2], sin A - sin B = 2 cos[(A+B)/2] sin[(A-B)/2], cos A + cos B = 2 cos[(A+B)/2] cos[(A-B)/2], cos A - cos B = -2 sin[(A+B)/2] sin[(A-B)/2]
  13. Inverse trigonometric functions: sin^-1 (x) = y if sin y = x and -π/2 ≤ y ≤ π/2, cos^-1 (x) = y if cos y = x and 0 ≤ y ≤ π, tan^-1 (x) = y if tan y = x and -π/2 < y < π/2
  14. Hyperbolic functions: sinh x = (e^x - e^-x) / 2, cosh x = (e^x + e^-x) / 2, tanh x = sinh x / cosh x, csch x = 1 / sinh x, sech x = 1 / cosh x, coth x = cosh x / sinh x

These formulas are essential in mathematics and are used in various fields, such as physics, engineering, and finance, among others.

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