Question

-. cos²x-sin²x = √3\2​

Answer 1

Відповідь: xR на файле

Answer 2

To solve the equation cos²x - sin²x = √3/2, we can use the trigonometric identity cos²x - sin²x = cos(2x). So the equation becomes:

cos(2x) = √3/2

To find the values of x that satisfy this equation, we need to find the angles whose cosine is equal to √3/2. These angles can be determined using the unit circle or a calculator.

The reference angle for √3/2 is π/6 (30 degrees). Therefore, the solutions for x can be found by adding or subtracting multiples of π/6. So we have:

2x = π/6 + 2πn or 2x = 11π/6 + 2πn

where n is an integer.

Now, solve for x:

x = (π/6)/2 + πn or x = (11π/6)/2 + πn

Simplifying:

x = π/12 + πn or x = 11π/12 + πn

where n is an integer.

These are the general solutions to the equation cos²x - sin²x = √3/2.