Let f(x)=tanx−tan3x+tan5x−tan7x+... where x∈(0, π4) then which of the following is/are true

∫ 0 π 6 f ( x ) = 1 8 , lt x → 0 − f ( x ) x = 1 , f ( x ) is an odd function

Let f ( x ) = tanx 1 + tan 2 x = 1 2 sin 2 x

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Let $f (x) = tanx - \tan^{3} x + \tan^{5} x - \tan^{7} x + . ..$ where $x \in (0, \frac{π}{4})$ then which of the following is/are true

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$\int_{0}^{\frac{π}{6}} f (x) = \frac{1}{8}$

$f' (\frac{π}{12}) = \frac{1}{2}$

$\underset{x \to 0 -}{lt} \frac{f (x)}{x} = 1$

$f (x)$ is an odd function

answer is A, C, D.

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Let $f (x) = \frac{tanx}{1 + \tan^{2} x} = \frac{1}{2} \sin 2 x$

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