Question

3sin2x-3sinxcosx+cos2x=0 Помогите пожалуйстаа!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

$3*2sinx*cosx-3sinx*cosx+(cos^{2}x-sin^{2}x)=0$
$3sinx*cosx+cos^{2}x-sin^{2}x=0$ - разделим обе части на квадрат косинуса (косинус не равен 0, т.к. косинус и синус не могут быть одновременно равными 0)
$3tgx+1-tg^{2}x=0$
$tg^{2}x-3tgx-1=0$

Замена: tgx=t

$t^{2}-3t-1=0, D=9+4=13$
$t_{1}= \frac{3+ \sqrt{13}}{2}$
$t_{2}= \frac{3- \sqrt{13}}{2}$

Вернемся к замене:
1) $tgx=\frac{3+ \sqrt{13}}{2}$
$x=acrtg(\frac{3+ \sqrt{13}}{2})+ \pi k$, k∈Z

2) $tgx=\frac{3- \sqrt{13}}{2}$
$x=acrtg(\frac{3- \sqrt{13}}{2})+ \pi k$, k∈Z

Answer 2

Solving the Trigonometric Equation 3sin(2x) - 3sin(x)cos(x) + cos(2x) = 0

To solve the trigonometric equation 3sin(2x) - 3sin(x)cos(x) + cos(2x) = 0, we can use trigonometric identities and properties to simplify and solve for the values of x.

Solution Steps:

1. Use Trigonometric Identities: - We can use trigonometric identities to simplify the equation and express it in terms of sine and cosine functions.

2. Factor and Solve: - After simplifying the equation, we can factor and solve for the values of x that satisfy the equation.

Solution:

Using the provided search results, we can see that the equation can be simplified and solved using trigonometric identities and properties. Here are the steps to solve the equation:

1. Simplify Using Trigonometric Identities: - The equation can be simplified using trigonometric identities such as the double-angle identities and the Pythagorean identity.

2. Factor and Solve for x: - After simplifying, we can factor the equation and solve for the values of x that satisfy the equation.

Based on the search results, the solutions involve using trigonometric identities and properties to simplify and solve the equation. The solutions involve expressing the equation in terms of sine and cosine functions and then factoring and solving for the values of x that satisfy the equation.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask!