Definite IntegrationHard

Question

Let  In = tan n x dx, then , .... are in  :

Options

A.A.P.
B.G.P.
C.H.P.
D.none

Solution

In +  In+2 = (tann x + tann+2 x)dx, n ≥ 2
= tann x  sec2 x dx =
∴ I2 + I4 = 1/3,  I3 + I5 = 1/4,  I4 + I6 = 1/5 etc.
∴
are in A.P.

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