WBJEE 2025 Math Paper

Telescoping product ⟶ a double-angle
One shows by induction (or by repeated half-angle/angle-doubling algebra) that
Plug in x=‌

π

16

:

Solve
We want tan(‌

2nπ

16

)=1. That means
The only power of two of the form 4m+1 is 1 itself, giving
2n=4‌‌⟹‌‌n=2,k=0.
Hence
f2(‌

π

16

)=tan(‌

22π

16

)=tan(‌

π

4

)=1