Trigonometric EquationHard

Question

I_n = tanⁿ x dx then

n [I_n + I_n-2] equals

Options

A.

B.1

C.∞

D.zero

Solution

tanⁿ x(1 + tan² x)dx =tanⁿ x sec² xdx =tⁿdt where t = tan x
I_n + I_{n + 2} = ; ⇒

n[I_n + I_n+2] =

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