If \({I_n} = \mathop \smallint \limits_0^{\pi /4} {\tan ^n}\theta d\theta\) then the following reduction formula exists:

\({I_n} + {I_{n - 2}} + \frac{1}{{n + 1}} = 0\)

\({I_n} + {I_{n - 2}} = \frac{1}{{n - 1}}\)

\({I_n} - {I_{n - 2}} = \frac{1}{{n + 1}}\)

\({I_n} - {I_{n - 2}} + \frac{1}{{n - 1}} = 0\)

If \({I_n} = \mathop \smallint \limits_0^{\pi /4} {\tan ^n}\theta d\th

1.	If \({I_n} = \mathop \smallint \limits_0^{\pi /4} {\tan ^n}\theta d\theta\) then the following reduction formula exists:
A.	\({I_n} + {I_{n - 2}} = \frac{1}{{n - 1}}\)
B.	\({I_n} + {I_{n - 2}} + \frac{1}{{n + 1}} = 0\)
C.	\({I_n} - {I_{n - 2}} = \frac{1}{{n + 1}}\)
D.	\({I_n} - {I_{n - 2}} + \frac{1}{{n - 1}} = 0\)
Answer» B. \({I_n} + {I_{n - 2}} + \frac{1}{{n + 1}} = 0\)

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