The problem involves verifying the identity arctan(x) + arctan(1/x) = π/2 using calculus theory, specifically through differentiation. Participants are exploring the relationship between the functions involved and their derivatives.
Participants are actively discussing the differentiation of the identity and exploring the implications of their findings. Some guidance has been offered regarding the differentiation process, and there is acknowledgment of the need to specify conditions for the variable x.
There is a hint provided in the original problem to differentiate the left side, and some participants note confusion regarding the steps involved in the differentiation. The discussion also touches on the behavior of the function across its domain, particularly for x ≠ 0.
chapsticks said:Homework Statement
Verify the identity:
arctanx + arctan(1/x)=∏/2
using calculus theory.
(Hint: Differentiate the left hand side of the identity)
Homework Equations
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The Attempt at a Solution
is this correct?
tan(arctanx + arctan(1/x))
= [tan(arctan(x)) + tan(arctan(1/x))][1 - tan(arctan(x))*tan(arctan(1/x))]
= [x + 1/x]/[1 - x*1/x] = (x + 1/x)/0 = oo
tan pi/2 = oo
chapsticks said:f'(x)=1/(1+x2) + -1/(x2+1) =0
for all x≠0
function is constant on domain
is this right?