Trigonometry Examples

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

Step 1

Rewrite $\csc (x - 1)$ in terms of sines and cosines.

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

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

One to any power is one.

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

Step 3

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

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

Step 4

Multiply by $1$ .

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

Step 5

Separate fractions.

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

Step 6

Convert from $\frac{1}{\sin^{2} (x - 1)}$ to $\csc^{2} (x - 1)$ .

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

Step 7

Divide $\sin^{2} (x)$ by $1$ .

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