Question

Prove that : tan2A = (sec2A+1)(sec²A-1)^1/2

Answer 1

sec 2A +1 = 1/cos 2A + 1 = (1+ cos 2A) /cos 2A
= (1 + 2cos^2 A -1) / cos 2A
= 2 cos ^2 A / cos 2A

sec^2 A - 1 = tan^2 A
(sec^2 A -1)^(1/2) = tan A

(2 cos^2 A / cos 2A) tan A
= 2 cos^2 A tan A / cos 2A
= 2 cos^2 A (sin A/cos A) / cos 2A
= 2 sin A cos A / cos 2A
= sin 2A / cos 2A
= tan 2A