What is expand e^{i(a+b)}+e^{-i(a+b)} ?

The solution to expand e^{i(a+b)}+e^{-i(a+b)} is 2cos(a+b)

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expand e^{i(a+b)}+e^{-i(a+b)}

expand

e^{i (a + b)} + e^{- i (a + b)}

2 cos (a + b)

Solution steps

e^{i (a + b)} + e^{- i (a + b)}

e^{i (a + b)} = cos (a + b) + i sin (a + b)

e^{- i (a + b)} = cos (a + b) - i sin (a + b)

= cos (a + b) + i sin (a + b) + cos (a + b) - i sin (a + b)

Group like terms

= cos (a + b) + cos (a + b) + i sin (a + b) - i sin (a + b)

Add similar elements:

cos (a + b) + cos (a + b) = 2 cos (a + b)

= 2 cos (a + b) + i sin (a + b) - i sin (a + b)

Add similar elements:

i sin (a + b) - i sin (a + b) = 0

= 2 cos (a + b)

\frac{( 2 x + 3 ) ( 3 x - 1 )}{2}

\frac{1}{( ( 2 x - 3 ) ( 2 x - 1 ) )}

\frac{5}{( 2 x - 4 ) ^{2}}

- \frac{2 ( - x + 2 )}{( x + 1 ) ^{4}}

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

What is expand e^{i(a+b)}+e^{-i(a+b)} ?
The solution to expand e^{i(a+b)}+e^{-i(a+b)} is 2cos(a+b)