Solving the Equation sin2x = 0: Solutions and Techniques

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The equation sin2x represents the sine of 2x, where x is an angle measured in radians

The equation sin2x represents the sine of 2x, where x is an angle measured in radians.

To solve this equation, we can use the double-angle identity for sine, which states that sin(2θ) = 2sin(θ)cos(θ).

In this case, our angle is 2x, so the equation sin(2x) = 2sin(x)cos(x).

Now, let’s set up and solve the equation.

sin(2x) = 2sin(x)cos(x)

We can rewrite sin(x)cos(x) as 1/2 * 2sin(x)cos(x) to fit the form of the double-angle identity.

sin(2x) = 2 * (1/2 * 2sin(x)cos(x))

simplifying this gives us:

sin(2x) = sin(x)cos(x)

Now we have a trigonometric equation. To solve for x, we need to find the possible values of x that satisfy this equation.

One way to approach this is to use the trigonometric identity sin(2x) = 2sin(x)cos(x) and equate the corresponding parts on both sides:

sin(x)cos(x) = sin(x)cos(x)

Now, we can see that this equation is satisfied for any angle x. So, there are infinitely many solutions to this equation. The values of x can be any real number.

Therefore, the solutions to the equation sin(2x) = 0 are x = kπ, where k is an integer.

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