Question

(√3-2sin x) (cos^2 x-sin^2 x)=0​

Answer 1

Ответ:

x = ((-1)^n)(Pi/3)+Pi*n и x = Pi/4 + (Pi*n)/2

Объяснение:

там либо первая либо вторая скобка равна нулю, а дальше очевидные математические преобразования

Answer 2

To solve the equation (√3 - 2sin x)(cos^2 x - sin^2 x) = 0, we can use the zero product property. According to the zero product property, if the product of two factors is equal to zero, then at least one of the factors must be zero.

So, we have two factors here:

1. (√3 - 2sin x)
2. (cos^2 x - sin^2 x)

To find the solutions, we need to set each factor to zero and solve for x.

Setting the first factor to zero:

√3 - 2sin x = 0

Now, isolate sin x:

2sin x = √3

sin x = √3 / 2

The first solution for x is when sin x is equal to √3 / 2. We can find this solution using the unit circle or by knowing the common angles that satisfy this condition (e.g., π/3 or 60 degrees).

Setting the second factor to zero:

cos^2 x - sin^2 x = 0

Now, we can use the trigonometric identity cos^2 x - sin^2 x = cos(2x):

cos(2x) = 0

To find the solutions for cos(2x) = 0, we can use the unit circle or knowledge of trigonometric angles (e.g., π/2 or 90 degrees, and 3π/2 or 270 degrees).

So, the solutions to the original equation (√3 - 2sin x)(cos^2 x - sin^2 x) = 0 are:

1. sin x = √3 / 2 (e.g., x = π/3 or 60 degrees)
2. cos(2x) = 0 (e.g., x = π/4 or 45 degrees, x = 3π/4 or 135 degrees, x = 5π/4 or 225 degrees, x = 7π/4 or 315 degrees)

Remember that there might be additional solutions that fall outside the range of 0 to 2π or 0 to 360 degrees depending on the context of the problem.