Calculus Examples

$\cot (\frac{5 π}{4}) - \cot (\frac{3 π}{4})$

Step 1

Simplify each term.

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Step 1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\cot (\frac{π}{4}) - \cot (\frac{3 π}{4})$

Step 1.2

The exact value of $\cot (\frac{π}{4})$ is $1$ .

$1 - \cot (\frac{3 π}{4})$

Step 1.3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cotangent is negative in the second quadrant.

$1 - - \cot (\frac{π}{4})$

Step 1.4

The exact value of $\cot (\frac{π}{4})$ is $1$ .

$1 - (- 1 \cdot 1)$

Step 1.5

Multiply $- (- 1 \cdot 1)$ .

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Step 1.5.1

Multiply $- 1$ by $1$ .

$1 - - 1$

Step 1.5.2

Multiply $- 1$ by $- 1$ .

$1 + 1$

Step 2

Add $1$ and $1$ .

$2$