Question

3sin2x+8cos^2 x=7 уравнение

Answer 1

Ответ:ну как то так

Объяснение:

Answer 2

To solve the trigonometric equation 3sin^2(x) + 8cos^2(x) = 7, we'll use trigonometric identities to simplify the expression and then solve for x.

Step 1: Apply the Pythagorean identity: sin^2(x) + cos^2(x) = 1.

Step 2: Rearrange the equation using the Pythagorean identity:

3sin^2(x) + 8cos^2(x) = 7 3(1 - cos^2(x)) + 8cos^2(x) = 7 3 - 3cos^2(x) + 8cos^2(x) = 7 3cos^2(x) - 3 = 7 3cos^2(x) = 10

Step 3: Divide both sides by 3 to isolate cos^2(x):

cos^2(x) = 10/3

Step 4: Take the square root of both sides:

cos(x) = ±√(10/3)

Step 5: Find the two possible solutions for x:

a) When cos(x) = √(10/3): x = arccos(√(10/3))

b) When cos(x) = -√(10/3): x = arccos(-√(10/3))

Please note that arccos represents the inverse cosine function, and it produces results in radians. Depending on the desired domain and the range of x values, the solutions can be adjusted. Also, keep in mind that trigonometric equations often have multiple solutions due to the periodic nature of trigonometric functions.