Question

The real part of $\cos h\left(\alpha +i\beta \right)$is

• A. $\cos h\left(\alpha \right)\cos \left(\beta \right)$
• B. $\cos \left(\alpha \right)\cos \left(\beta \right)$
• C. $\cos \left(\alpha \right)\cos h\left(\beta \right)$
• D. $\sin \left(\alpha \right)\sin h\left(\beta \right)$

Answer 1

The correct option is A

$\cos h\left(\alpha \right)\cos \left(\beta \right)$

Explanation for the correct option:

Given expression is $\cos h\left(\alpha +i\beta \right)$ let us expand the identity and then we will find the real part of it so,

$$\begin{gathered} \cos h\left(\alpha +i\beta \right)=\cos h\left(\alpha \right)+\cos h\left(i\beta \right)+\sin h\left(\alpha \right)\sin h\left(i\beta \right) \\ \cos h\left(\alpha +i\beta \right)=\cos h\left(\alpha \right)\cos \left(\beta \right)+i\sin h\left(\alpha \right)\sin \left(\beta \right) \end{gathered}$$

So, we see that real part of given expression is $\cos h\left(\alpha \right)\cos \left(\beta \right)$

Hence, the correct option is (A)