Prove that- (1+sec2A )(1+sec4A)=cotA
Answer (1)
12th Jan, 2020
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
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