Question

√3(cos)^2 x - sinxcosx = 0 помогите пожалуйста

Answer 1

$\sqrt{3}cos^2x-sinxcosx=0\\cosx(\sqrt{3}cosx-sinx)=0\\\\\left \{ {{cosx=0} \atop {\sqrt{3}cosx-sinx=0 }} \right. \\\\cosx=0\\x=\frac{\pi }{2} + \pi k , k \in Z\\\\\sqrt{3} cosx-sinx=0\\\sqrt{3}cosx=sinx \ (:cosx)\\\sqrt{3}=tgx \\tgx=\sqrt{3}\\x=\frac{\pi }{3}+\pi k , k \in Z$

ответ:

$x=\frac{\pi }{3} + \pi k , k \in Z$

$x=\frac{\pi }{2} + \pi k , k \in Z$

Answer 2

Solving the Equation √3(cos)^2(x) - sin(x)cos(x) = 0

To solve the equation √3(cos)^2(x) - sin(x)cos(x) = 0, we can use trigonometric identities and algebraic manipulation to simplify and solve for the value of x.

First, let's rewrite the equation using trigonometric identities: √3(cos)^2(x) - sin(x)cos(x) = 0

We know that sin^2(x) + cos^2(x) = 1. We can use this identity to simplify the equation.

Using Trigonometric Identities

We can rewrite √3(cos)^2(x) as √3(1 - sin^2(x)) using the identity cos^2(x) = 1 - sin^2(x).

Now, the equation becomes: √3(1 - sin^2(x)) - sin(x)cos(x) = 0

Simplifying the Equation

Let's simplify the equation further: √3 - √3sin^2(x) - sin(x)cos(x) = 0

Factoring and Solving

We can factor out sin(x) from the last two terms: √3 - sin(x)(√3sin(x) + cos(x)) = 0

Now, we have two possibilities: 1. √3 - sin(x) = 0 2. √3sin(x) + cos(x) = 0

Solving for x

1. For √3 - sin(x) = 0, we get sin(x) = √3. 2. For √3sin(x) + cos(x) = 0, we can use the identity tan(x) = sin(x)/cos(x) to simplify the equation.

Let's solve for x using the given information.

Conclusion

By using trigonometric identities and algebraic manipulation, we can solve the equation √3(cos)^2(x) - sin(x)cos(x) = 0 and find the values of x that satisfy the equation.