# Determine tg [pi/2 - arctg(1/2)] .

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tg(pi/2 -arctg(1/2)

We know that :

ctg (x)= tg(pi/2 - x)

==> tg(pi/2 -arctg(1/2)= ctg (arctg(1/2)

= ctg(arc ctg (2)

= 2

To detrmine tg {pi/2 - arctg (1/2)}

Solution:

We know that tan (pi-x) = 1/tanx

So tan {pi/2-arctan (1/2)} = 1/ tan {arc tan(1/2)}

= 1/tan (1/2)

= 1/tan (0.5radians)

= 1/tan (28.64789 deg)

= 1.83049 nearly

We'll use the formula tg(pi/2 - k) = ctg k.

Now, we'll apply the formula, where k = arctg(1/2)

tg[pi/2 - arctg(1/2)] = ctg [arctg(1/2)]

But ctg k = 1/tg k

ctg [arctg(1/2)]=1/tg(arctg(1/2))=1/(1/2)=2