What is the value of arctan(1)+arctan(1/1) ?

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

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arctan(1)+arctan(1/1)

arctan (1) + arctan (\frac{1}{1})

\frac{π}{2}

Decimal Notation

90

Solution steps

arctan (1) + arctan (\frac{1}{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}

Use the following trivial identity:

arctan (\frac{1}{1}) = \frac{π}{4}

arctan (\frac{1}{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}

= \frac{π}{4} + \frac{π}{4}

Simplify

\frac{π}{4} + \frac{π}{4} : \frac{π}{2}

\frac{π}{4} + \frac{π}{4}

Apply rule

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

= \frac{π + π}{4}

Add similar elements:

π + π = 2 π

= \frac{2 π}{4}

Cancel the common factor:

2

= \frac{π}{2}

= \frac{π}{2}

- 3 sin (2 (\frac{7 π}{4}))

arcsin (\frac{1}{2} 3)

\frac{1 + tan ^{2} ( 67. 5 ^{\circ} )}{1 - tan ^{2} ( 67. 5 ^{\circ} )}

sin (53. 1^{\circ}) (25) - (9.8) (3)

\frac{600 sin ( 12 7 ^{\circ} )}{sin ( 11 3 ^{\circ} )}

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