=c^{2}\left(\frac{e^{x}+e^{-x}}{2}+\frac{e^{x}-e^{-x}}{2}\right)^{2} e^{-2 x}

^^20(5)(b)^^20\quad j\cos (\alpha+j\beta)

\cos (\alpha+j \beta)=\cos \alpha \cos (j \beta)-\sin \alpha \sin (j \beta)

j \cos (\alpha+j \beta)=j \cos \alpha \cdot \cos (j \beta)-\sin \alpha j \sin (j \beta)

\text { Now } j \sin (j \beta)=j \cdot\left(\frac{e^{j(j \beta)}-e^{-j(j \beta)}}{2 j}\right)

\& \quad j \cos (j \beta)=j \cdot\left(\frac{e^{j(j \beta)}+e^{-j(j \beta)}}{2}\right)

=-\sinh \beta


=j \cosh \beta

10 ; \quad j \cos (\alpha+j \beta)=j \cos \alpha \cosh \beta-\sin \alpha(-\sinh \beta)


=j \cdot\left(\frac{e^{-\beta}+e^{\beta}}{2}\right)

i \cos (\alpha+j \beta)=\sinh \beta \sin \alpha+j \cosh \beta(01 \alpha

(a+b)^{2} e^{-2 x}=(c \cosh x+c \sinh x)^{2} e^{-2 x}

=c^{2}\left(\cosh ^{2} x-\sinh ^{2} x\right)

=c^{2}\left(e^{x}\right)^{2} e^{-2 x}=c^{2}

=c^{2}(\cos h x+\sinh x)(\cos h x-\sinh x)

a^{2}-b^{2}=(c \cosh x)^{2}-(c \sinh x)^{2}

=c^{2}\left(\frac{e^{k}+e^{-x}}{2}+\frac{e^{x} e^{-x}}{2}\right)\left(\frac{e^{x}+e^{-x}}{2}-\frac{e^{x}-e^{-x}}{2}\right)

=c^{2} \cdot \operatorname{so}(a+b)^{2} e^{-2 x}=a^{2}-b^{2}




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