How do you find the exact value of $arctan (1) + arctan (2) + arctan (3)$ $arctan(1) + arctan(2) + arctan(3)$ ?

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How do you find the exact value of $arctan (1) + arctan (2) + arctan (3)$ $arctan(1) + arctan(2) + arctan(3)$ ?

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Answer 1 · 2015-06-26T03:13:47

Answer is 0.

Explanation:

$arctan x + arctan y + arctan z = arctan$ $arctanx+arctany+arctanz=arctan$ $\frac{x + y + z - x y z}{1 - x y - y z - z x}$ $(x+y+z-xyz)/(1-xy-yz-zx)$

Let x= $1$ $1$ , $y = 2$ $y=2$ , $z = 3$ $z=3$

$arctan (1) + arctan (2) + arctan (3) =$ $arctan(1)+arctan(2)+arctan(3)=$

$= arctan$ $=arctan$ $\frac{(1) + (2) + (3) - (1 \cdot 2 \cdot 3)}{1 - (1 \cdot 2) (2 \cdot 3) (3 \cdot 1)}$ $((1)+(2)+(3)-(1*2*3))/(1-(1*2)(2*3)(3*1)$

$= arctan (\frac{0}{- 35})$ $=arctan(0/(-35))$

$= arctan (0)$ $=arctan(0)$

$= arctan (tan 0))$ $=arctan(tan0))$ [from angle table]

$=cancel(arctan)cancel(tan)((0))$

$=0$

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How do you find the exact value of $arctan (1) + arctan (2) + arctan (3)$ $arctan(1) + arctan(2) + arctan(3)$ ?

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How do you find the exact value of arctan(1) + arctan(2) + arctan(3) arctan(1)+arctan(2)+arctan(3)arctan(1) + arctan(2) + arctan(3) ?

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How do you find the exact value of $arctan (1) + arctan (2) + arctan (3)$ $arctan(1) + arctan(2) + arctan(3)$ ?