Trigonometry Examples

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

Step 1

Apply pythagorean identity.

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

Step 2

Apply pythagorean identity.

$\csc^{2} (x)$

Step 3

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

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

Step 4

Simplify the expression.

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Step 4.1

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

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

Step 4.2

One to any power is one.

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

Step 4.3

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

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

Step 5

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

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

Step 6

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

$\csc^{2} (x)$