Question

1)-1sin^2a-cos^2a+1 2) ctga-cos^2a•ctga 3) sin^2a/cos^2•ctga 4) ctg^2+cos^2a/sin^2a Срочноооооо плиз ПОМОГИТЕ

Answer 1

Ответ:

1)-1sin²a-cos²a+1=-sin²a-cos²a+sin²a+cos²a=0

1=sin²a+cos²a

2)ctga-cos²a×ctga°ctga(1-cos²a)=ctga×sin²a=cosa/sina×sin²a=cosa×sina

1-cos²a=sin²a

3)sin²a/cos²a×ctga=sin²a×cosa/cos²a×sina=sin²acosa/cos²a=sin²a/cos²a×cosa/cos²a=tg²a×secx

4)ctg²a+cos²a/sin²a=ctg²a+ctg²a=2ctg²a

Answer 2

1. The expression is:

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

Let's simplify it step by step:

We know that sin^2(a) + cos^2(a) = 1 (based on the Pythagorean identity). Therefore, -sin^2(a) - cos^2(a) + 1 = 1 - 1 = 0.

So, the simplified expression is 0.

2. The expression is:

ctg(a) - cos^2(a) * ctg(a)

To simplify it, let's factor out ctg(a):

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

Using the Pythagorean identity, we know that 1 - cos^2(a) = sin^2(a). Therefore, the expression becomes:

ctg(a) * sin^2(a)

3. The expression is:

sin^2(a) / cos^2(a) * ctg(a)

To simplify it, let's rewrite ctg(a) as cos(a) / sin(a):

sin^2(a) / cos^2(a) * (cos(a) / sin(a))

Canceling out common factors:

(sin(a) / cos(a)) * (cos(a) / sin(a))

The sin(a) in the numerator and the cos(a) in the denominator cancel each other out:

1

So, the simplified expression is 1.

4. The expression is:

ctg^2(a) + cos^2(a) / sin^2(a)

To simplify it, let's rewrite ctg^2(a) as (cos^2(a) / sin^2(a)):

(cos^2(a) / sin^2(a)) + cos^2(a) / sin^2(a)

Combining the two fractions with the same denominator:

(2 * cos^2(a)) / sin^2(a)

So, the simplified expression is (2 * cos^2(a)) / sin^2(a).