Trigonometry Examples

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

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

Step 1

Multiply by

1

$1$ .

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

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

Step 2

Simplify with factoring out.

Tap for more steps...

Step 2.1

Factor

sin (x)

$\sin (x)$ out of

sin (x) {cot}^{2} (x)

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

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

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

Step 2.2

Factor

sin (x)

$\sin (x)$ out of

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

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

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

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

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

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

Step 3

Apply pythagorean identity.

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

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

Step 4

Rewrite

csc (x)

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

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

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

Step 5

Simplify the expression.

Tap for more steps...

Step 5.1

Apply the product rule to

\frac{1}{sin (x)}

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

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

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

Step 5.2

One to any power is one.

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

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

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

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

Step 6

Cancel the common factor of

sin (x)

$\sin (x)$ .

Tap for more steps...

Step 6.1

Factor

sin (x)

$\sin (x)$ out of

{sin}^{2} (x)

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

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

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

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

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

Step 7

Convert from

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

$\csc (x)$ .

$\csc (x)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$