Question

Тригонометричні формули додавання аргументів

Answer 1

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Answer 2

Trigonometric Addition Formulas

Trigonometric addition formulas are used to express the sum or difference of two trigonometric functions in terms of a single trigonometric function. These formulas are particularly useful in simplifying trigonometric expressions and solving trigonometric equations.

One of the most commonly used trigonometric addition formulas is the sum of angles formula for sine:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

where a and b are angles.

Another important trigonometric addition formula is the sum of angles formula for cosine:

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

These formulas can be derived using the properties of right triangles and the unit circle.

It's worth noting that there are also subtraction formulas for sine and cosine, which can be obtained by substituting -b for b in the addition formulas:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

These formulas can be used to find the sine, cosine, or tangent of the sum or difference of two angles.

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