What is factor e^{ix}+e^{-ix} ?

The solution to factor e^{ix}+e^{-ix} is (cos(-x)+isin(-x))(cos(2x)+isin(2x)+1)

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factor e^{ix}+e^{-ix}

factor

e^{i x} + e^{- i x}

(cos (- x) + i sin (- x)) (cos (2 x) + i sin (2 x) + 1)

Solution steps

e^{i x} + e^{- i x}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

e^{i x} = e^{- i x} e^{2 i x}

= e^{- i x} e^{2 i x} + e^{- i x}

Factor out common term

e^{- i x}

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

Refine

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

- 2 x = - 10

24 x^{2} - 24 x = 0

(7 x^{6})^{2}

(x - 4) (2 x - 6) = 0

- p x + p x^{2} - 2 p

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