Question

(1+cos)*ctg^2 альфа *(1- cos альфа)

Answer 1

(1 + cosα)*(1 - cosα)*ctg²α = (1 - cos²α) * ctg²α = sin²α * (cos²α / sin²α) = cos²α

Ответ: cos²α

Answer 2

The expression you provided seems to be a combination of trigonometric functions. Let's break it down step by step:

(1+cos)ctg^2 α(1- cos α)

To simplify this expression, let's start by expanding the trigonometric functions:

(1 + cos α) * ctg^2 α * (1 - cos α)

Next, let's rewrite ctg^2 α as 1/tan^2 α:

(1 + cos α) * (1/tan^2 α) * (1 - cos α)

Now, let's simplify further by multiplying the terms:

(1 + cos α) * (1 - cos α) / tan^2 α

Using the identity (a + b)(a - b) = a^2 - b^2, we can simplify the numerator:

(1 - cos^2 α) / tan^2 α

Now, using the Pythagorean identity sin^2 α + cos^2 α = 1, we can replace cos^2 α with 1 - sin^2 α:

(1 - (1 - sin^2 α)) / tan^2 α

Simplifying further:

sin^2 α / tan^2 α

Using the identity tan α = sin α / cos α:

(sin^2 α) / (sin^2 α / cos^2 α)

The sine squared cancels out:

1 / (1 / cos^2 α)

Inverting the fraction:

cos^2 α

So, the simplified expression is just cos^2 α.