Trigonometry Examples

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

Step 1

Apply pythagorean identity.

$\cos^{2} (x) \csc^{2} (x)$

Step 2

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

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

Step 3

Simplify the expression.

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Step 3.1

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

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

Step 3.2

One to any power is one.

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

Step 4

Combine $\cos^{2} (x)$ and $\frac{1}{\sin^{2} (x)}$ .

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

Step 5

Convert from $\frac{\cos^{2} (x)}{\sin^{2} (x)}$ to $\cot^{2} (x)$ .

$\cot^{2} (x)$