Trigonometry Examples

$\sin (x) \cos (x) \tan (x) = 1 - \cos^{2} (x)$

Step 1

Start on the left side.

$\sin (x) \cos (x) \tan (x)$

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

Factor $\cos (x)$ out of $\sin (x) \cos (x)$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$\sin (x) \sin (x)$

Step 2.3

Raise $\sin (x)$ to the power of $1$ .

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

Step 2.4

Raise $\sin (x)$ to the power of $1$ .

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

Step 2.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sin (x)}^{1 + 1}$

Step 2.6

Add $1$ and $1$ .

$\sin^{2} (x)$

Step 3

Apply Pythagorean identity in reverse.

$1 - \cos^{2} (x)$

Step 4

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

$\sin (x) \cos (x) \tan (x) = 1 - \cos^{2} (x)$ is an identity