Question

1.(sina / 1-cosa) + (sina/1+cosa); 2. sin2a /1+cosa; 3. ctg b(1-cosb); 4. 1+cos2a / 2 cosa; 5. 1- cos2a / 2sina ; 6. tga ( 1+cos2a)

Answer 1

1.(sin²a+1+2cosa+cos²a)/(sina)(1+cosa)=(2+2cosa)/sina(1+cosa)=2(1+cosa)/sina(1+cosa)=2/sina

ИЛИ

sina/(1+cosa)+(1+cosa)/sina-2/sina=0; sina/(1+cosa)+(cosa-1)/sina=0; ((sina)^2+(cosa)^2-1)/(sina(1+cosa))=0;(1-1)/(sina(1+cosa))=0

Answer 2

1. (sin(a) + 1)/(cosa): To simplify this expression, we can start by factoring out a common term, which is 1. We have:

(sin(a) + 1)/(cosa) = 1*(sin(a) + 1)/(cosa)

Next, we can simplify the expression by dividing each term separately:

1*(sin(a) + 1)/(cosa) = sin(a)/(cosa) + 1/(cosa)

Using the identity sin(a)/cosa = tan(a), we can rewrite the expression as:

tan(a) + sec(a)

2. sin^2(a)/(1+cosa): To simplify this expression, we can start by using the identity sin^2(a) = 1 - cos^2(a):

sin^2(a)/(1+cosa) = (1 - cos^2(a))/(1+cosa)

Next, we can factor out a common term, which is 1:

(1 - cos^2(a))/(1+cosa) = 1*(1 - cos^2(a))/(1+cosa)

Now, we can simplify the expression by dividing each term separately:

1*(1 - cos^2(a))/(1+cosa) = (1 - cos^2(a))/(1+cosa)

Using the identity 1 - cos^2(a) = sin^2(a), we can rewrite the expression as:

sin^2(a)/(1+cosa)

3. ctg(b(1-cosb)): The expression ctg(b(1-cosb)) represents the cotangent of the angle b times (1 - cos(b)).

4. (1 + cos^2(a))/(2cosa): To simplify this expression, we can start by factoring out a common term, which is cos^2(a). We have:

(1 + cos^2(a))/(2cosa) = cos^2(a) * (1 + 1/cos^2(a))/(2cosa)

Next, we can simplify the expression by dividing each term separately:

cos^2(a) * (1 + 1/cos^2(a))/(2cosa) = (cos^2(a) + 1/cos^2(a))/(2cosa)

Using the identity cos^2(a) + 1/cos^2(a) = sec^2(a), we can rewrite the expression as:

sec^2(a)/(2cosa)

5. (1 - cos^2(a))/(2sin(a)): To simplify this expression, we can start by factoring out a common term, which is 1 - cos^2(a). We have:

(1 - cos^2(a))/(2sin(a)) = (1 - cos^2(a))/(2sin(a))

Using the identity 1 - cos^2(a) = sin^2(a), we can rewrite the expression as:

sin^2(a)/(2sin(a))

Simplifying further, we have:

sin(a)/2

6. tga(1 + cos^2(a)): The expression tga(1 + cos^2(a)) represents the tangent of the angle a times (1 + cos^2(a)).