Question

Sin2x√cosx = 0

Answer 1

$sin2x \sqrt{cosx}=0 \\ 2sinx*cosx \sqrt{cosx} =0 \\ sinx=0 => x= \pi k \\ cosx=0 => x= \frac{ \pi }{2} + \pi k$

объединив ответы получим  $x= \frac{ \pi k}{2}$

Answer 2

To solve the equation sin(2x)√cos(x) = 0, we need to find the values of x that satisfy the equation.

First, let's break down the equation and solve each part individually:

1. sin(2x) = 0: This equation is satisfied when 2x is an integer multiple of π (i.e., 2x = nπ, where n is an integer). Therefore, x = nπ/2, where n is an integer.

2. √cos(x) = 0: The square root of any non-negative number (such as cos(x)) cannot be zero. Therefore, this equation has no solution.

Now, let's combine the solutions from both equations:

The values of x that satisfy the equation sin(2x)√cos(x) = 0 are x = nπ/2, where n is an integer.