what is the answer Find the exact value if any of the follo

what is the answer ?

Find the exact value, if any, of the following composite function. If there is no value, say it is \"not defined.\" Do not use a calculator. tan tan Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression ) R. Not defined

Solution

Ans: arctan (tan x) = x if and only if x belongs to (-pi/2, pi/2).

We know that tan x has period of pi. So we reduce to a value in the interval (-pi/2, pi/2) by subtracting an

integral multiple of pi so that new x belongs to (-pi/2, pi/2).

Here, x = -5pi/2 which can be reduced to -pi/2 by adding 2pi but arctan (tanx) is not defined for x = -pi/2.