Solve. 2sin x cos x=sin x

Write Equation: First, let's write down the given equation. 2sin x cos x = sin xSubtract and Rearrange: Now, we subtract sin x from both sides to move all terms involving x to one side of the equation. 2sin x cos x - sin x = 0Factor Out: Factor out sin x from the left side of the equation. sin x (2cos x - 1) = 0Set Equal to Zero: Set each factor equal to zero to find the solutions for x. sin x = 0 and 2cos x - 1 = 0Solve sin x = 0: Solve the first equation sin x = 0. The solutions for x are the angles where the sine function equals zero. x = nπ, where n is an integer.Solve cos x = 1/2: Solve the second equation 2cos x - 1 = 0. Add 1 to both sides and then divide by 2. cos x = 1/2Find the values of x where the cosine function equals 1/2. x = π/3 + 2nπ or x = 5π/3 + 2nπ, where n is an integer.

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Solve. $\newline$ $2 \sin x \cos x=\sin x$

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Algebra 1

Solve linear equations with variables on both sides

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Q. Solve.

\newline

2 \sin x \cos x=\sin x

Write Equation: First, let's write down the given equation. $\newline$ $2\sin x \cos x = \sin x$
Subtract and Rearrange: Now, we subtract $\sin x$ from both sides to move all terms involving $x$ to one side of the equation. $\newline$ $2\sin x \cos x - \sin x = 0$
Factor Out: Factor out $\sin x$ from the left side of the equation. $\sin x (2\cos x - 1) = 0$
Set Equal to Zero: Set each factor equal to zero to find the solutions for $x$ . $\sin x = 0$ and $2\cos x - 1 = 0$
Solve $\sin x = 0$ : Solve the first equation $\sin x = 0$ . The solutions for $x$ are the angles where the sine function equals zero. $x = n\pi$ , where $n$ is an integer.
Solve $\cos x = \frac{1}{2}$ : Solve the second equation $2\cos x - 1 = 0$ . $\newline$ Add $1$ to both sides and then divide by $2$ . $\newline$ $\cos x = \frac{1}{2}$
Solve $\cos x = \frac{1}{2}$ : Solve the second equation $2\cos x - 1 = 0$ . Add $1$ to both sides and then divide by $2$ . $\cos x = \frac{1}{2}$ Find the values of $x$ where the cosine function equals $\frac{1}{2}$ . $x = \frac{\pi}{3} + 2n\pi$ or $x = \frac{5\pi}{3} + 2n\pi$ , where $n$ is an integer.