Inverse Tan (1/x) + Inverse tan (x) = Pi/2 ? (1 Viewer)

Bloodstriker

Member
Joined
May 12, 2011
Messages
202
Location
Big Shell
Gender
Male
HSC
2012
My textbook hasn't listed this one, (only has the one for inverse sin + inverse cos) but i'm pretty sure it's correct. Can anyone clarify?
 

Caboufram

Member
Joined
Nov 3, 2011
Messages
137
Gender
Undisclosed
HSC
N/A
it's because

assume tan(a) = 1/x

and tan(b) = x

effectively they'd be in the same right angled triangle, with sides, "1", "x" and hypotenuse "(x^2+1)^1/2.

Thus,
a+b+90 = 180
giving
a+b=90

which means

arctan(1/x) + arctan(x) = 90

which is in effect, pi/2
 

Caboufram

Member
Joined
Nov 3, 2011
Messages
137
Gender
Undisclosed
HSC
N/A
I kind of just used that method on the spot, not sure if it's the correct proof. But I think it's important you realise they're the same triangle.
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top