Question

Cos x/3 cos П/6+sin x/3 sin П/6=-1​

Answer 1

Ответ:

фото

Объяснение:

Answer 2

To solve the equation cos(x/3) cos(π/6) + sin(x/3) sin(π/6) = -1, we can use the identity:

cos(a - b) = cos(a) cos(b) + sin(a) sin(b)

Comparing this identity with the given equation, we can see that a = x/3 and b = π/6. So we can rewrite the equation as:

cos(x/3 - π/6) = -1

Now we need to find the values of x that satisfy this equation.

To solve for x, we can use the inverse cosine function (also known as arccos or cos^(-1)). Taking the inverse cosine of both sides, we have:

x/3 - π/6 = arccos(-1)

The inverse cosine of -1 is π, so the equation becomes:

x/3 - π/6 = π

Next, we can solve for x by isolating it on one side of the equation:

x/3 = π + π/6

x/3 = 7π/6

Multiplying both sides by 3, we get:

x = 7π/2

Therefore, the solution to the equation cos(x/3) cos(π/6) + sin(x/3) sin(π/6) = -1 is x = 7π/2.