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= (sec 8A -1) / (sec 4A -1)=> [(1 - cos 8A)/ cos 8A] / [(1 - cos 4A)/ cos 4A]=> [2 sin² 4A / 2 sin² 2A] * [cos 4A / cos 8A]=> [(2 sin 4A * cos 4A) * sin 4A / cos 8A] / [2 sin² 2A]=> [(sin 8A / cos 8A) * sin 4A] / [2 sin² 2A]=> tan 8A * (sin 4A / 2 sin² 2A)=> tan 8A * (2sin 2A * cos 2A / 2 sin² 2A)=> tan 8A * ( cos 2A / sin 2A)=> tan 8A * cot 2A => tan 8A / tan 2A
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Arun (askIITians forum expert)
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