Question

Cos(60°+2)×cos(60°-2)​

Answer 1

правильный ответ

cos(4) - 1

2 4

Answer 2

To calculate the value of cos(60° + 2) × cos(60° - 2), you can use the trigonometric identities.

First, convert degrees to radians because trigonometric functions typically work with radians:

60 degrees = π/3 radians 2 degrees = 2π/180 radians = π/90 radians

Now, you can calculate the values:

cos(60° + 2) = cos(π/3 + π/90) cos(60° - 2) = cos(π/3 - π/90)

Use the sum and difference identities for cosine:

cos(A + B) = cos(A)cos(B) - sin(A)sin(B) cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

In this case, A = π/3 and B = π/90:

cos(60° + 2) = cos(π/3)cos(π/90) - sin(π/3)sin(π/90) cos(60° - 2) = cos(π/3)cos(π/90) + sin(π/3)sin(π/90)

Now, use the values of cos(π/3) and sin(π/3), which are known:

cos(π/3) = 1/2 sin(π/3) = √3/2

And use the values of cos(π/90) and sin(π/90), which can be calculated as follows:

cos(π/90) = cos(π/3 - π/90) = cos(π/3)cos(π/90) + sin(π/3)sin(π/90) sin(π/90) = sin(π/3 - π/90) = sin(π/3)cos(π/90) - cos(π/3)sin(π/90)

Now, calculate cos(π/90) and sin(π/90):

cos(π/90) = (1/2)cos(π/90) + (√3/2)sin(π/90) sin(π/90) = (√3/2)cos(π/90) - (1/2)sin(π/90)

Let's denote cos(π/90) as "x" and sin(π/90) as "y." Then, we have the following system of equations:

x = (1/2)x + (√3/2)y y = (√3/2)x - (1/2)y

Solve this system of equations for x and y. First, isolate y in the second equation:

y = (√3/2)x - (1/2)y (3/2)y = (√3/2)x y = (√3/3)x

Now, substitute this expression for y into the first equation:

x = (1/2)x + (√3/2)y x = (1/2)x + (√3/2)(√3/3)x x = (1/2)x + (√3/6)x

Now, isolate x:

(2/2 - 1/2)x = (√3/6)x (1/2)x = (√3/6)x

Divide both sides by (1/2):

x = (√3/6)x

Now, you can solve for x:

(1 - √3/6)x = 0

x = 0

Now that you have the value of x, you can find the value of y using the second equation:

y = (√3/3)x y = (√3/3)(0) y = 0

So, cos(π/90) = x = 0 and sin(π/90) = y = 0.

Now, you can calculate the values of cos(60° + 2) and cos(60° - 2):

cos(60° + 2) = (1/2)(0) - (√3/2)(0) = 0 cos(60° - 2) = (1/2)(0) + (√3/2)(0) = 0

Therefore, cos(60° + 2) × cos(60° - 2) = 0.