Question

Tg альфа + ctg альфа

Answer 1

tgA * ctgA = 1
Их умножают, а не складывают

Answer 2

Получается вот так

tga *ctga = 1

Answer 3

To simplify the expression "Tg(α) + Ctg(α)," we need to express the trigonometric functions in terms of basic trigonometric ratios like sine and cosine.

Tg(α) is the tangent of angle α, defined as the ratio of the length of the side opposite to α (opposite side) to the length of the side adjacent to α (adjacent side). The formula for tangent is:

Tg(α) = sin(α) / cos(α)

Ctg(α) is the cotangent of angle α, defined as the reciprocal of the tangent of α. The formula for cotangent is:

Ctg(α) = 1 / Tg(α) = cos(α) / sin(α)

Now let's combine the two expressions:

Tg(α) + Ctg(α) = (sin(α) / cos(α)) + (cos(α) / sin(α))

To simplify further, we need a common denominator, which is cos(α) * sin(α):

Tg(α) + Ctg(α) = (sin^2(α) + cos^2(α)) / (cos(α) * sin(α))

Since sin^2(α) + cos^2(α) = 1 (from the Pythagorean identity), the expression becomes:

Tg(α) + Ctg(α) = 1 / (cos(α) * sin(α))

There you have the simplified expression for Tg(α) + Ctg(α), which is 1 / (cos(α) * sin(α)).