Trigonometry Examples

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

Step 1

Apply pythagorean identity.

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

Step 2

Cancel the common factor of $\csc (x)$ and $\csc^{2} (x)$ .

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Step 2.1

Multiply by $1$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $\csc (x)$ out of $\csc^{2} (x)$ .

$\frac{\csc (x) \cdot 1}{\csc (x) \csc (x)}$

Step 2.2.2

Cancel the common factor.

$\frac{\csc (x) \cdot 1}{\csc (x) \csc (x)}$

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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

Step 4

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

$1 \sin (x)$

Step 5

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

$\sin (x)$