tangent eats my head
Geometry
Level
2
Given that (1+tan 1°)(1+tan 2°)..........(1+tan 45°)= then the value of n is equal to
37
19
23
29
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
A + B = 45°
tan(A + B) = tan45° = 1
tanA + tanB = 1 - tanAtanB
1+ tanA + tanB + tanAtanB = 2
(1 + tanA)(1 + tanB) = 2
(1 + tan1°)(1 + tan2°)(1 + tan3°)...(1 + tan45°)
= [(1 + tan1°)(1 + tan44°)][(1 + tan2°)(1 + tan43°)]...[(1 + tan22°)(1 + tan23°)] (1 + tan45°)
= 2^23
n = 23