Question

If $z=i\ln \left(2-\sqrt{3}\right)$, then $cosz=$

• A. $0$
• B. $1$
• C. $2$
• D. None of these

Answer 1

Answer: (A)

$0$

Given, $\cos \left(z\right)=\cos \left(i\ln (2-\sqrt{3})\right)$

$\because \cos ix=\cosh x\therefore \cos \left(i\ln (2-\sqrt{3})\right)=\cosh \left(\ln (2-\sqrt{3})\right)$

Also, $\cosh x=\frac{1}{2}(e^x+e^{-x})$$\therefore \cosh \left(\ln (2-\sqrt{3})\right)=\frac{1}{2}(e^{\ln (2-\sqrt{3})}+e^{-\ln (2-\sqrt{3})})=\frac{1}{2}\{\ln (2-\sqrt{3})-\ln (2-\sqrt{3})\}=0$