If \( f^{\prime}(x)=\tan ^{-1}(\sec x+\tan x), x \in\left(-\frac{\pi}{2} \frac{\pi}{2}\right) \)....

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If \( f^{\prime}(x)=\tan ^{-1}(\sec x+\tan x), x \in\left(-\frac{\pi}{2} \frac{\pi}{2}\right) \) and
\( \mathrm{P} \)
\( f(0)=0 \), then the value of \( f(1) \) is
(1) \( \frac{\pi+1}{4} \)
(2) \( \frac{\pi-1}{4} \)
(3) \( \frac{\pi+1}{2} \)
(4) 0



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