What is the value of arctan(1)-arctan(-1) ?

The value of arctan(1)-arctan(-1) is pi/2

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arctan(1)-arctan(-1)

arctan (1) - arctan (- 1)

\frac{π}{2}

Decimal Notation

90

Solution steps

arctan (1) - arctan (- 1)

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 1) = - arctan (1)

= arctan (1) - (- arctan (1))

Simplify

= 2 arctan (1)

Use the following trivial identity:

arctan (1) = \frac{π}{4}

arctan (1)

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{4}

= 2 \cdot \frac{π}{4}

Simplify

2 \cdot \frac{π}{4} : \frac{π}{2}

2 \cdot \frac{π}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{4}

Cancel the common factor:

2

= \frac{π}{2}

= \frac{π}{2}

tan (1 3^{\circ})

cos (\frac{6 π}{4})

sin^{2} (8 0^{\circ})

cos (- 16 5^{\circ})

sin^{2} (- 1)

What is the value of arctan(1)-arctan(-1) ?
The value of arctan(1)-arctan(-1) is pi/2