What is the value of 2arctan(sqrt(1)) ?

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

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2arctan(sqrt(1))

2 arctan (1)

\frac{π}{2}

Decimal Notation

90

Solution steps

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}

cot (arccos (\frac{3}{2}))

sec (4 9^{\circ})

75 sin (3 5^{\circ})

sin (arccos (\frac{4}{5}) - arctan (\frac{5}{12}))

sec^{2} (18 0^{\circ})