Question

1+ctg^2 (-a)-1/sin(1,5pi-2a)

Answer 1

1+ctg²(a)=1+cos²(a)/sin²(a)!=sin²(a)+cos²(a)/sin²(a)отсюда sin²(a)=1-cos²(a)подставляем

1-соs²(a)+cos²(a)/sin²(a)=1/sin²(a)

Answer 2

To simplify the expression, let's first rewrite it step by step:

1. Start with the given expression: 1 + ctg^2(-a) - 1/sin(1.5pi - 2a)

2. Recall that ctg^2(-a) is the square of the cotangent function. Since ctg(-a) is the reciprocal of tan(-a), we can rewrite it as: ctg^2(-a) = (1/tan(-a))^2

3. The trigonometric identities for tangent are: tan(-a) = -tan(a) and tan(pi - a) = -tan(a). Therefore, tan(1.5pi - 2a) = -tan(2a - 0.5pi).

4. Now, we can rewrite the expression as follows: 1 + (1/tan(-a))^2 - 1/sin(1.5pi - 2a) = 1 + (1/(-tan(a)))^2 - 1/sin(2a - 0.5pi)

5. Simplify the squared reciprocal term: (1/(-tan(a)))^2 = (-1/tan(a))^2 = 1/tan^2(a)

6. Now, we have: 1 + 1/tan^2(a) - 1/sin(2a - 0.5pi)

7. Recall the trigonometric identity for tangent squared: 1 + tan^2(a) = sec^2(a). Therefore, 1/tan^2(a) = sec^2(a) - 1.

8. Substitute back into the expression: 1 + (sec^2(a) - 1) - 1/sin(2a - 0.5pi)

9. Simplify further: 1 + sec^2(a) - 1 - 1/sin(2a - 0.5pi) = sec^2(a) - 1 - csc(2a - 0.5pi)

So, the simplified expression is: sec^2(a) - 1 - csc(2a - 0.5pi)