Dear Aspirant,

I have check the question it is misprint but I have tried to prove the Result hope this will help you.

here is the your answer:

recall your half-angle formula:

tan(x/2) = sinx/(1+cosx)

Now, we have

1+sec2A = (1+cos2A)/cos2A
= 1/[cos2A/(1+cos2A)]
= 1/[sin2A/(1+cos2A) * cos2A/sin2A]
= 1/(tanA cot2A)
= tan2A/tanA ---------------- (1)
Now we can see that
1+sec4A = tan4A/tan2A--------------------(2)

now we multiply eq.1 and 2, we get

(1+sec2A)(1+sec4A) = cot A*tanA