Trigonometry Examples

$\sin (x) - \sin (x) \cos^{2} (x) = \sin^{3} (x)$

Step 1

Start on the left side.

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

Step 2

Apply Pythagorean identity.

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Step 2.1

Multiply by $1$ .

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

Step 2.2

Factor $\sin (x)$ out of $- \sin (x) \cos^{2} (x)$ .

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

Step 2.3

Factor $\sin (x)$ out of $\sin (x) \cdot 1 + \sin (x) (- 1 \cos^{2} (x))$ .

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

Step 2.4

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

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

Step 2.5

Apply pythagorean identity.

$\sin (x) \cdot \sin^{2} (x)$

Step 3

Multiply $\sin (x)$ by ${\sin (x)}^{2}$ by adding the exponents.

$\sin^{3} (x)$

Step 4

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

$\sin (x) - \sin (x) \cos^{2} (x) = \sin^{3} (x)$ is an identity