Question

4cos^2x-1=0 тригонометрия​

Answer 1

4cos²2x-1=0

4cos²2x=1

cos²2x=1/4

cos2x=±(1/2)

cosx=1/2

x= ±pi/3 + 2pi*n, n принадлежит Z

cosx= -1,2

x= ±2pi/3 + 2pi*n, n принадлежит Z

Answer 2

Ответ: 4соs²x-1=0

4cos²x=1

cos²x= 1/4

cos= ±1/2

cos1/2. cos -1/2

x= pi/3 +2pin. х= 2pi/3+ 2pin

x= pin/6. x= 3pin/6

Объяснение:

Answer 3

To solve the trigonometric equation 4cos^2(x) - 1 = 0, we'll follow these steps:

Step 1: Recognize the trigonometric identity. Step 2: Solve for cos(x). Step 3: Find the values of x.

Step 1: Recognize the trigonometric identity. The equation 4cos^2(x) - 1 = 0 can be recognized as the double-angle identity for cosine:

cos(2x) = 2cos^2(x) - 1

Step 2: Solve for cos(x). Rewrite the equation using the double-angle identity:

cos(2x) = 1

Step 3: Find the values of x. To solve for x, we need to find the angles whose cosine is equal to 1. Remember that the cosine function has a range of [-1, 1].

When does cos(x) = 1? The only angle that satisfies this condition is 0 degrees (or 0 radians). In trigonometry, this is represented as:

x = 0 + 2πn

where n is an integer (n = 0, ±1, ±2, ...).

So the general solutions to the equation are:

x = 0 + 2πn, where n is an integer.