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Consider the real numbers p and q such that −1<p,q<1.
Find the range of possible values of
arctanp
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arctanp−arctanq
Prove that arctanp−arctanq≡arctan(1+pqp−q).
Let a∈Z,a≥1.
Show that 0<arctan(a+1)−arctan(a−1)<2π.
Using the identity in (b), verify that arctan(a+1)−arctan(a−1)=arctan(a22)
Using the results from (b) and (d), and the method of mathematical induction, prove that
for all n∈N.
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