Trigonometry Examples

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

Step 1

Apply pythagorean identity.

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

Step 2

Simplify with factoring out.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

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

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

Step 4

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (x)}$ .

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

Step 5

Multiply $\sin (x)$ by $1$ .

$\sin^{2} (x)$