Algebra Examples

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

Step 1

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

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

Step 2

Rearrange terms.

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

Step 3

Apply pythagorean identity.

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

Step 4

Apply pythagorean identity.

$\csc^{2} (x)$

Step 5

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

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

Step 6

Simplify the expression.

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Step 6.1

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

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

Step 6.2

One to any power is one.

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

Step 6.3

Rewrite $1$ as $1^{2}$ .

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

Step 7

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

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

Step 8

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

$\csc^{2} (x)$