Trigonometry Examples

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

Multiply by $1$ .

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

Simplify with factoring out.

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

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

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

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

Apply pythagorean identity.

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

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

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

Apply the product rule to $\frac{1}{\sin (x)}$ .

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

One to any power is one.

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

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

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Write $\sin (x)$ as a fraction with denominator $1$ .

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

Factor out the greatest common factor $\sin (x)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{1}{1}$ and $\frac{1}{\sin (x)}$ .

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

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\csc (x)$

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