Precalculus Examples

$\sin (x) \csc (x) = 1$

Step 1

Simplify the left side.

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Step 1.1

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 1.1.1

Reorder $\sin (x)$ and $\csc (x)$ .

$\csc (x) \sin (x) = 1$

Step 1.1.2

Rewrite $\sin (x) \csc (x)$ in terms of sines and cosines.

$\frac{1}{\sin (x)} \sin (x) = 1$

Step 1.1.3

Cancel the common factors.

$1 = 1$

Step 2

Since $1 = 1$ , the equation will always be true for any value of $x$ .

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$