Question

· If cosh x = sec 0 then prove that tanh?
2
= tan
2.​

Answer 1

We know Tanh2 x/2

= cosh x - 1 / cosh x + 1

= sec 0 - 1 / sec 0 + 1

= 1 - cos 0 / 1 - cos 0 = 2 sin²(0/2) / 2cos²(0/2)

= Tan2 θ/2

∴ Tanh2 x/2 = Tan2 θ/2

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