If \( \cos (1-i)=a+i b \), where \( a, b \in R \) and \( i=\sqrt{-1} \), then
(a) \( a=\frac{1}{...
If \( \cos (1-i)=a+i b \), where \( a, b \in R \) and \( i=\sqrt{-1} \), then
(a) \( a=\frac{1}{2}\left(e-\frac{1}{e}\right) \cos 1, b=\frac{1}{2}\left(e+\frac{1}{e}\right) \sin 1 \)
(b) \( a=\frac{1}{2}\left(e+\frac{1}{e}\right) \cos 1, b=\frac{1}{2}\left(e-\frac{1}{e}\right) \sin 1 \)
(c) \( a=\frac{1}{2}\left(e+\frac{1}{e}\right) \cos 1, b=\frac{1}{2}\left(e+\frac{1}{e}\right) \sin 1 \)
(d) \( a=\frac{1}{2}\left(e-\frac{1}{e}\right) \cos 1, b=\frac{1}{2}\left(e-\frac{1}{e}\right) \sin 1 \)
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