Trigonometry Examples

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

Step 1

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

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Step 1.1

Multiply by $1$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Apply pythagorean identity.

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

Step 3

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

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

Step 4

Simplify the expression.

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Step 4.1

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

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

Step 4.2

One to any power is one.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

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

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$1$