Trigonometry Examples

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

Step 1

Start on the left side.

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

Step 2

Convert to sines and cosines.

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Step 2.1

Write $\tan (x)$ in sines and cosines using the quotient identity.

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

Step 2.2

Apply the reciprocal identity to $\csc (x)$ .

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

Step 3

Simplify.

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Step 3.1

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

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

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

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Step 3.2.1

Cancel the common factor.

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

Step 3.2.2

Rewrite the expression.

$1$

Step 4

Because the two sides have been shown to be equivalent, the equation is an identity.

$(\cos (x)) (\tan (x)) (\csc (x)) = 1$ is an identity