find the value of (tan 2 tan 4 tan 6....tan 88)

Hello Palak if A + B = 90 then tan A tan B = 1
How? tan A * tan (90 - A) = tan A * cot A = tan A * 1/tan A = 1
So in our series 2 and 88, (4,86), (6,84), (8,82), (10,80) .....(44,46).
As they satisfy A+B = 90, all factors finally get reduced to 1