Question

$\cos h\left(2\right)+\sin h\left(2\right)=?$

• A. $\frac{1}{e}$
• B. $e$
• C. $\frac{1}{e^2}$
• D. $e^2$

Answer 1

The correct option is D

$e^2$

Explanation for the correct option:

Formula used: $\mathit{c}\mathit{o}\mathit{s}\mathbf{}\mathit{h}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}\frac{{\mathbf{e}}^{\mathbf{x}}\mathbf{+}{\mathbf{e}}^{\mathbf{-}\mathit{x}}}{\mathbf{2}}\mathbf{,}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{h}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}\frac{{\mathbf{e}}^{\mathbf{x}}\mathbf{-}{\mathbf{e}}^{\mathbf{-}\mathit{x}}}{\mathbf{2}}$

$\Rightarrow$ $\cos h\left(2\right)+\sin h\left(2\right)=\left(\frac{e^2+e^{-2}}{2}\right)+\left(\frac{e^2-e^{-2}}{2}\right)$

$=\frac{2e^2}{2}$

$={\mathit{e}}^{\mathbf{2}}$

Hence, Option ‘D’ is Correct.