Trigonometry Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Apply pythagorean identity.

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

Step 3

Cancel the common factor of $\sin^{2} (x)$ and $\sin (x)$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $\sin (x)$ by $1$ .

$\sin (x)$