Question

Корень из 3 - корень из 12*sin^2(13pi/12) = ?

Answer 1

Ответ:

1,5

Пошаговое объяснение:

√3-2√3sin^2(П+П/12)=√3(1-2sin^2(П/12))=

=√3(1-1+cosП/6)=√3*√3/2=3/2

Answer 2

To simplify the expression, let's start step by step:

1. First, let's simplify the term inside the square root: sin^2(13pi/12)

To find the value of sin^2(13pi/12), we can use the trigonometric identity: sin^2(theta) + cos^2(theta) = 1

In this case, theta = 13pi/12. However, it's more convenient to work with the complementary angle, which is theta_complementary = pi - theta. Therefore: sin^2(theta) = 1 - cos^2(theta)

Now, we need to find cos(13pi/12): To do that, we can use the fact that cos(theta) = cos(-theta), which allows us to rewrite cos(13pi/12) as cos(-pi/12).

2. Now, we find cos(-pi/12): cos(-pi/12) = cos(pi/12) (since cos(-x) = cos(x))

3. Next, we need to find cos(pi/12): To do that, we can use the trigonometric identity: cos(2x) = 2cos^2(x) - 1 Rearrange the terms: cos^2(x) = (cos(2x) + 1) / 2

In this case, x = pi/6 (because pi/12 = pi/6 + pi/6)

4. Now, we find cos(pi/6): cos(pi/6) = sqrt(3)/2

5. Plug the value of cos(pi/6) back to find cos^2(13pi/12): cos^2(13pi/12) = (cos(2 * pi/6) + 1) / 2 = (cos(pi/3) + 1) / 2 = (1/2 + 1) / 2 = 3/4

6. Now, we find sin^2(13pi/12): sin^2(13pi/12) = 1 - cos^2(13pi/12) = 1 - 3/4 = 1/4

7. Finally, let's simplify the original expression: sqrt(3) - sqrt(12 * sin^2(13pi/12)) = sqrt(3) - sqrt(12 * (1/4)) = sqrt(3) - sqrt(3) = 0

So, the result of the expression is 0.