簡約 1/2 (e^{ix}+e^{-ix})

解

簡約

\frac{1}{2} (e^{i x} + e^{- i x})

cos (x)

解答ステップ

\frac{1}{2} (e^{i x} + e^{- i x})

e^{i x} = cos (x) + i sin (x)

e^{- i x} = cos (x) - i sin (x)

= \frac{1}{2} (cos (x) + i sin (x) + cos (x) - i sin (x))

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ( cos ( x ) + sin ( x ) i + cos ( x ) - i sin ( x ) )}{2}

1 \cdot (cos (x) + sin (x) i + cos (x) - i sin (x)) = 2 cos (x)

= \frac{2 cos ( x )}{2}

数を割る:

\frac{2}{2} = 1

= cos (x)