Algebra Examples

cot (\frac{π}{2} - x)

$\cot (\frac{π}{2} - x)$

Step 1

Apply the difference of angles identity.

\frac{cot (\frac{π}{2}) cot (x) + 1}{cot (x) - cot (\frac{π}{2})}

$\frac{\cot (\frac{π}{2}) \cot (x) + 1}{\cot (x) - \cot (\frac{π}{2})}$

Step 2

Simplify the numerator.

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Step 2.1

The exact value of

cot (\frac{π}{2})

$\cot (\frac{π}{2})$ is

0

$0$ .

\frac{0 cot (x) + 1}{cot (x) - cot (\frac{π}{2})}

$\frac{0 \cot (x) + 1}{\cot (x) - \cot (\frac{π}{2})}$

Step 2.2

Multiply

0

$0$ by

cot (x)

$\cot (x)$ .

\frac{0 + 1}{cot (x) - cot (\frac{π}{2})}

$\frac{0 + 1}{\cot (x) - \cot (\frac{π}{2})}$

Step 2.3

Add

0

$0$ and

1

$1$ .

\frac{1}{cot (x) - cot (\frac{π}{2})}

$\frac{1}{\cot (x) - \cot (\frac{π}{2})}$

\frac{1}{cot (x) - cot (\frac{π}{2})}

$\frac{1}{\cot (x) - \cot (\frac{π}{2})}$

Step 3

Simplify the denominator.

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Step 3.1

The exact value of

cot (\frac{π}{2})

$\cot (\frac{π}{2})$ is

0

$0$ .

\frac{1}{cot (x) - 0}

$\frac{1}{\cot (x) - 0}$

Step 3.2

Multiply

- 1

$- 1$ by

0

$0$ .

\frac{1}{cot (x) + 0}

$\frac{1}{\cot (x) + 0}$

Step 3.3

Add

cot (x)

$\cot (x)$ and

0

$0$ .

\frac{1}{cot (x)}

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

\frac{1}{cot (x)}

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

Step 4

Rewrite

cot (x)

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

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

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

Step 5

Multiply by the reciprocal of the fraction to divide by

\frac{cos (x)}{sin (x)}

$\frac{\cos (x)}{\sin (x)}$ .

\frac{sin (x)}{cos (x)}

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

Step 6

Convert from

\frac{sin (x)}{cos (x)}

$\frac{\sin (x)}{\cos (x)}$ to

tan (x)

$\tan (x)$ .

tan (x)

$\tan (x)$