Question

(1 - cos a)²ctg²a - (cos²a - 1)​

Answer 1

Ответ:

sіn (а)2

Пошаговое объяснение:

Answer 2

Let's simplify the expression:

(1 - cos(a))^2 * cot(a)^2 - (cos(a)^2 - 1)

First, we can expand the square of the first term:

(1 - cos(a))^2 = (1 - cos(a))(1 - cos(a)) = 1 - 2cos(a) + cos(a)^2

Now, we can rewrite cot(a) in terms of sine and cosine:

cot(a) = 1/tan(a) = cos(a)/sin(a)

So, cot(a)^2 = (cos(a)/sin(a))^2 = cos(a)^2/sin(a)^2

Now, we can substitute this expression for cot(a)^2 into the equation:

(1 - 2cos(a) + cos(a)^2) * (cos(a)^2/sin(a)^2) - (cos(a)^2 - 1)

Next, we'll simplify the expression by multiplying both terms by sin(a)^2 to eliminate the denominators:

(1 - 2cos(a) + cos(a)^2) * cos(a)^2 - (cos(a)^2 - 1) * sin(a)^2

Now, distribute cos(a)^2 through the first term:

cos(a)^4 - 2cos(a)^3 + cos(a)^2 * cos(a)^2 - (cos(a)^2 - 1) * sin(a)^2

Simplify further:

cos(a)^4 - 2cos(a)^3 + cos(a)^4 - cos(a)^2 * sin(a)^2 + sin(a)^2

Now, combine like terms:

2cos(a)^4 - 2cos(a)^3 - cos(a)^2 * sin(a)^2 + sin(a)^2

Finally, you have the simplified expression:

2cos(a)^4 - 2cos(a)^3 - cos(a)^2 * sin(a)^2 + sin(a)^2

This is the simplified form of the expression (1 - cos(a))^2 * cot(a)^2 - (cos(a)^2 - 1).