Trigonometry Examples

$\frac{1}{\sin (2)} - \frac{1}{\tan (2)}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\tan (2)$ in terms of sines and cosines.

$\frac{1}{\sin (2)} - \frac{1}{\frac{\sin (2)}{\cos (2)}}$

Step 1.2

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (2)}{\cos (2)}$ .

$\frac{1}{\sin (2)} - (1 \frac{\cos (2)}{\sin (2)})$

Step 1.3

Write $1$ as a fraction with denominator $1$ .

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

Step 1.4

Simplify.

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Step 1.4.1

Rewrite the expression.

$\frac{1}{\sin (2)} - (1 \frac{\cos (2)}{\sin (2)})$

Step 1.4.2

Multiply $\frac{\cos (2)}{\sin (2)}$ by $1$ .

$\frac{1}{\sin (2)} - \frac{\cos (2)}{\sin (2)}$

Step 2

Simplify each term.

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Step 2.1

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

$\csc (2) - \frac{\cos (2)}{\sin (2)}$

Step 2.2

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

$\csc (2) - \cot (2)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\csc (2) - \cot (2)$

Decimal Form:

$0.01745506 \dots$