Question

If u = $log_e[tan(\frac{\pi}{4} + \frac{\theta}{2})]$ and if cos θ > 0, then prove that cosh u = sec θ.

Answer 1

Hi,

I have used different formulas to prove it.

One of the basic formulas of Trigonometry is

$tan(\alpha-\beta)=\frac{tan\alpha-tan\beta}{1+tan\alpha.tan\beta}$

I also used Half angle formulas.

I also used Double Angle identities in this proof.

Kindly see the attachment for the detailed Proof.

I hope it will help you.