Trigonometry Examples

2 \cos (x) \tan (x) \csc (x) = 2

$2 \cos (x) \tan (x) \csc (x) = 2$

Step 1

Simplify the left side.

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Step 1.1

Simplify

2 \cos (x) \tan (x) \csc (x)

$2 \cos (x) \tan (x) \csc (x)$ .

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Step 1.1.1

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

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Step 1.1.1.1

Add parentheses.

2 (\cos (x) \tan (x)) \csc (x) = 2

$2 (\cos (x) \tan (x)) \csc (x) = 2$

Step 1.1.1.2

Reorder

\cos (x)

$\cos (x)$ and

\tan (x)

$\tan (x)$ .

2 (\tan (x) \cos (x)) \csc (x) = 2

$2 (\tan (x) \cos (x)) \csc (x) = 2$

Step 1.1.1.3

Rewrite

2 \cos (x) \tan (x)

$2 \cos (x) \tan (x)$ in terms of sines and cosines.

2 (\frac{\sin (x)}{\cos (x)} \cos (x)) \csc (x) = 2

$2 (\frac{\sin (x)}{\cos (x)} \cos (x)) \csc (x) = 2$

Step 1.1.1.4

Cancel the common factors.

2 \sin (x) \csc (x) = 2

$2 \sin (x) \csc (x) = 2$

2 \sin (x) \csc (x) = 2

$2 \sin (x) \csc (x) = 2$

Step 1.1.2

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

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Step 1.1.2.1

Add parentheses.

2 (\sin (x) \csc (x)) = 2

$2 (\sin (x) \csc (x)) = 2$

Step 1.1.2.2

Reorder

\sin (x)

$\sin (x)$ and

\csc (x)

$\csc (x)$ .

2 (\csc (x) \sin (x)) = 2

$2 (\csc (x) \sin (x)) = 2$

Step 1.1.2.3

Rewrite

2 \sin (x) \csc (x)

$2 \sin (x) \csc (x)$ in terms of sines and cosines.

2 (\frac{1}{\sin (x)} \sin (x)) = 2

$2 (\frac{1}{\sin (x)} \sin (x)) = 2$

Step 1.1.2.4

Cancel the common factors.

2 \cdot 1 = 2

$2 \cdot 1 = 2$

2 \cdot 1 = 2

$2 \cdot 1 = 2$

Step 1.1.3

Multiply

2

$2$ by

1

$1$ .

2 = 2

$2 = 2$

2 = 2

$2 = 2$

2 = 2

$2 = 2$

Step 2

Since

2 = 2

$2 = 2$ , the equation will always be true for any value of

x

$x$ .

All real numbers

Step 3

The result can be shown in multiple forms.

All real numbers

Interval Notation:

(- \infty, \infty)

$(- \infty, \infty)$