Inverse trig (1 Viewer)

[Hipeople]

Hi, can someone show me how to do c). The answer is π/2 but I just don’t see how I can prove it.

 

[cossine]

Hi, can someone show me how to do c). The answer is π/2 but I just don’t see how I can prove it.

You can draw a triangle. For completeness draw two triangles one in the first quadrant and second quadrant.

Then make use of the period to generalise your result.

 

[d.goomeister]

Hi you might not need help anymore but:
Let A = arctanx
Therefore tanA = x
Using the identity Cot(90 - x) = tanx (will use pi/2 = 90 for easier visibility)
x = cot(90-A)
arccotx = 90-A
sub arctanx = A
arccotx = 90-arctanx
therefore arctanx+arccotx = 90 (pi/2)

 

[ISAM77]