Question

Sin^2x-3sin x cos x+2cos^2x=0

Answer 1

Ответ:

Объяснение:

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Answer 2

To solve the equation sin^2(x) - 3sin(x)cos(x) + 2cos^2(x) = 0, we can use trigonometric identities to simplify it and then solve for x. Here's how you can do it:

Start with the given equation: sin^2(x) - 3sin(x)cos(x) + 2cos^2(x) = 0

Now, we can use the trigonometric identity sin^2(x) + cos^2(x) = 1 to simplify the equation: 1 - 3sin(x)cos(x) = 0

Next, let's use another trigonometric identity, which is sin(2x) = 2sin(x)cos(x): 1 - 3sin(2x) = 0

Now, isolate sin(2x): 3sin(2x) = 1

Divide both sides by 3: sin(2x) = 1/3

Now, we have sin(2x) = 1/3. To solve for x, we can take the arcsin (inverse sine) of both sides:

2x = arcsin(1/3)

Now, divide both sides by 2 to solve for x: x = (1/2)arcsin(1/3)

So, the solution to the equation sin^2(x) - 3sin(x)cos(x) + 2cos^2(x) = 0 is: x = (1/2)arcsin(1/3) + kπ, where k is an integer.