Trigonometry Examples

$2 \arccos (x + 2) \arccos (x) = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$\arccos (x + 2) = 0$

$\arccos (x) = 0$

Step 2

Set $\arccos (x + 2)$ equal to $0$ and solve for $x$ .

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Step 2.1

Set $\arccos (x + 2)$ equal to $0$ .

$\arccos (x + 2) = 0$

Step 2.2

Solve $\arccos (x + 2) = 0$ for $x$ .

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Step 2.2.1

Take the inverse arccosine of both sides of the equation to extract $x$ from inside the arccosine.

$x + 2 = \cos (0)$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

The exact value of $\cos (0)$ is $1$ .

$x + 2 = 1$

Step 2.2.3

Move all terms not containing $x$ to the right side of the equation.

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Step 2.2.3.1

Subtract $2$ from both sides of the equation.

$x = 1 - 2$

Step 2.2.3.2

Subtract $2$ from $1$ .

$x = - 1$

Step 3

Set $\arccos (x)$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $\arccos (x)$ equal to $0$ .

$\arccos (x) = 0$

Step 3.2

Solve $\arccos (x) = 0$ for $x$ .

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Step 3.2.1

Take the inverse arccosine of both sides of the equation to extract $x$ from inside the arccosine.

$x = \cos (0)$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

The exact value of $\cos (0)$ is $1$ .

$x = 1$

Step 4

The final solution is all the values that make $2 \arccos (x + 2) \arccos (x) = 0$ true.

$x = - 1, 1$

Step 5

Exclude the solutions that do not make $2 \arccos (x + 2) \arccos (x) = 0$ true.

$x = - 1$