Question

If $\cos (x+iy)=A+iB$, then $A=$

• A. cos x cos hy
• B. sin x sin hy
• C. – sin x sin hy
• D. cos x sin hy

Answer 1

The correct option is A

cos x cos hy

Find the value of $A$:

Given, $\cos (x+iy)=A+iB$

$\Rightarrow$$\cos x\cos \left(iy\right)–\sin x\sin \left(iy\right)=A+iB$ $\left[\because cos\left(A+B\right)=cosAcosB-sinAsinB)\right]$

$\Rightarrow$$\cos x\cos hy–i\sin x\sin hy=A+iB$

By Compare real part of the above equation, we get

$\mathit{A}\mathbf{}\mathbf{=}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathbf{}\mathit{x}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathbf{}\mathit{h}\mathit{y}$

Hence, Option ‘A’ is Correct.