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

[Bloodstriker]

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]

Yes, yes that is correct.

 

[Caboufram]

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

 

[Bloodstriker]

Do we need to know the proof?

 

[Caboufram]

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.

 

[bobmcbob365]