Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

$\csc^{2} (x) + \frac{1}{\cos^{2} (x)}$

Step 4

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

$\csc^{2} (x) + \frac{1^{2}}{\cos^{2} (x)}$

Step 5

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

$\csc^{2} (x) + {(\frac{1}{\cos (x)})}^{2}$

Step 6

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

$\csc^{2} (x) + \sec^{2} (x)$