Trigonometry Examples

$\sqrt{3} \csc (x - 2) = 0$

Step 1

Divide each term in $\sqrt{3} \csc (x - 2) = 0$ by $\sqrt{3}$ and simplify.

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Step 1.1

Divide each term in $\sqrt{3} \csc (x - 2) = 0$ by $\sqrt{3}$ .

$\frac{\sqrt{3} \csc (x - 2)}{\sqrt{3}} = \frac{0}{\sqrt{3}}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $\sqrt{3}$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{\sqrt{3} \csc (x - 2)}{\sqrt{3}} = \frac{0}{\sqrt{3}}$

Step 1.2.1.2

Divide $\csc (x - 2)$ by $1$ .

$\csc (x - 2) = \frac{0}{\sqrt{3}}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $0$ by $\sqrt{3}$ .

$\csc (x - 2) = 0$

Step 2

The range of cosecant is $y \leq - 1$ and $y \geq 1$ . Since $0$ does not fall in this range, there is no solution.

No solution