Trigonometry Examples

$\cos (x) \csc (x) \tan (x) = 1$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\cos (x) \csc (x) \tan (x)$ .

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Step 1.1.1

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

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

Step 1.1.2

Combine $\cos (x)$ and $\frac{1}{\sin (x)}$ .

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

Step 1.1.3

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

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

Step 1.1.4

Cancel the common factor of $\cos (x)$ .

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Step 1.1.4.1

Cancel the common factor.

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

Step 1.1.4.2

Rewrite the expression.

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

Step 1.1.5

Cancel the common factor of $\sin (x)$ .

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Step 1.1.5.1

Cancel the common factor.

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

Step 1.1.5.2

Rewrite the expression.

$1 = 1$

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:

$(- \infty, \infty)$