Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite

$1$ as

$1^{2}$ .

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

Step 1.2

Rewrite

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

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

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

Step 1.3

Rewrite

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

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

Step 1.4

Multiply by the reciprocal of the fraction to divide by

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

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

Step 1.5

Multiply

$\sin (x)$ by

$1$ .

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

Step 2

Apply pythagorean identity.

$\cos^{2} (x)$