Question

If tanh x = sin theta, show that sinh x = tan theta, cosh x = sec theta .
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Answer 1

Answer:

⇒1−tanh2(x/2)1+tanh2(x/2)=secθ ⇒tanh2(x /2)=secθ+1secθ−1=1+cosθ1−cosθ ⇒tanh 2(x/2)=2cos2θ/22sin2θ/2=tan2(θ/2).