Question

(2-2/sin^2 (пи+альфа)(1/cos^2(альфа-пи)-1)

Answer 1

2((sin^2(a)-1)/sin^2(a))((1-cos^2(a))/cos^2(a))=2ctg^2(a)*tg^2(a)=2

Answer 2

Let's simplify the given expression step by step:

1. The value of π is approximately 3.14159.

2. Let's rewrite the expression with the given values: (2 - 2/sin^2(π + α)) * (1/cos^2(α - π) - 1)

3. Notice that sin(π + α) = sin(π) * cos(α) + cos(π) * sin(α) = 0 * cos(α) + (-1) * sin(α) = -sin(α) Also, cos(α - π) = cos(α) * cos(π) + sin(α) * sin(π) = -cos(α)

Now, the expression becomes:

(2 - 2/(-sin^2(α))) * (1/((-cos(α))^2) - 1)

4. Simplify the expression further:

(2 + 2/sin^2(α)) * (1/cos^2(α) - 1)

5. Now, let's manipulate the second part of the expression: 1/cos^2(α) - 1 = 1/cos^2(α) - cos^2(α)/cos^2(α) = (1 - cos^2(α))/cos^2(α) = sin^2(α)/cos^2(α) = tan^2(α)

6. Substitute this back into the expression:

(2 + 2/sin^2(α)) * tan^2(α)

7. Now, let's simplify further: 2 + 2/sin^2(α) = 2(sin^2(α) + 1)/sin^2(α) = (2sin^2(α) + 2)/sin^2(α) = 2(1 - cos^2(α))/sin^2(α) = 2tan^2(α)

So the final simplified expression is:

2tan^2(α) * tan^2(α) = 2tan^4(α)

Therefore, the simplified expression is 2tan^4(α).