en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 1/2 (e^{ix}+e^{-ix})

Solution

simplify

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

Solution

cos (x)

Solution steps

\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))

Multiply fractions:

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}

Divide the numbers:

\frac{2}{2} = 1

= cos (x)

Popular Examples

expand a/((a+b)+b(a+b))expand

\frac{a}{( a + b ) + b ( a + b )}

simplify 4\H(udx+xdu)simplify

4 H (u d x + x d u)

expand (x(1+x))/2 expand

\frac{x ( 1 + x )}{2}

expand (eu+u)^2 expand

(e u + u)^{2}

expand ((k+1)(2k^2+k+6))/6 expand

\frac{( k + 1 ) ( 2 k ^{2} + k + 6 )}{6}

Frequently Asked Questions (FAQ)

What is 1/2 (e^{ix}+e^{-ix}) ?
The solution to 1/2 (e^{ix}+e^{-ix}) is cos(x)