Question

(1-tga)cos2a= (1+tga)(1-sin2a)

Answer 1

Ответ:

(1-tga)cos2a= (1+tga)(1-sin2a)

cosa*(1- sina/cosa)cos2a= cosa*(1+ sina/cosa)(1-sin2a)

(cosa-sina)cos2a=(cosa+sina)( 1-sin2a)

(cosa-sina) (cos^2a-sin^2a)=(cosa+sina)( sin^2a+cos^2a-2sinacosa)

(cosa-sina) (cosa-sina) (cosa+sina)= (cosa+sina) (cosa-sina) ^2

(cosa+sina) (cosa-sina) ^2=(cosa+sina) (cosa-sina) ^2

Пошаговое объяснение:

Answer 2

Let's solve the equation (1 - tga)cos(2a) = (1 + tga)(1 - sin(2a)) for the variable "a."

First, let's simplify the equation step by step:

1. Expand the right side of the equation using the trigonometric identity sin(2a) = 2sin(a)cos(a):

(1 - tga)cos(2a) = (1 + tga)(1 - 2sin(a)cos(a))

2. Distribute (1 + tga) on the right side:

(1 - tga)cos(2a) = 1 - 2sin(a)cos(a) + tga - 2tgasin(a)cos(a)

3. Now, let's isolate the terms containing tga:

(1 - tga)cos(2a) - tga + 2tgasin(a)cos(a) = 1 - 2sin(a)cos(a)

4. Next, factor out tga from the left side:

tga(1 - cos(2a)) + 2tgasin(a)cos(a) = 1 - 2sin(a)cos(a)

5. Now, factor out common terms on the left side:

tga(1 - cos(2a) + 2sin(a)cos(a)) = 1 - 2sin(a)cos(a)

6. Divide both sides by the expression in parentheses:

tga = (1 - 2sin(a)cos(a)) / (1 - cos(2a) + 2sin(a)cos(a))

7. Now, let's simplify further. Use the trigonometric identity cos(2a) = 2cos^2(a) - 1:

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

8. Continue simplifying:

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

9. Factor out a 2 from the denominator:

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

10. Use the Pythagorean identity sin^2(a) + cos^2(a) = 1 to simplify the denominator:

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

11. Substitute sin^2(a) = 1 - cos^2(a):

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

Now, you have the equation in terms of "a" and "tga." Depending on the values of "tga" and the constraints of the problem, you may need to further simplify or solve for "a" if that's the objective.