What is (e^{iw}-e^{-iw})/(e^{iw)+e^{-iw}} ?

The solution to (e^{iw}-e^{-iw})/(e^{iw)+e^{-iw}} is (isin(w))/(cos(w))

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simplify (e^{iw}-e^{-iw})/(e^{iw)+e^{-iw}}

simplify

\frac{e ^{i w} - e ^{- i w}}{e ^{i w} + e ^{- i w}}

\frac{i sin ( w )}{cos ( w )}

Solution steps

\frac{e ^{i w} - e ^{- i w}}{e ^{i w} + e ^{- i w}}

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

= \frac{cos ( w ) + i sin ( w ) - ( cos ( - w ) + i sin ( - w ) )}{e ^{i w} + e ^{- i w}}

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

= \frac{cos ( w ) + i sin ( w ) - ( cos ( - w ) + i sin ( - w ) )}{cos ( w ) + i sin ( w ) + cos ( - w ) + i sin ( - w )}

cos (- w) = cos (w)

sin (- w) i = - i sin (w)

= \frac{cos ( w ) + i sin ( w ) - ( cos ( - w ) + i sin ( - w ) )}{cos ( w ) + i sin ( w ) + cos ( w ) - i sin ( w )}

- (cos (- w) + sin (- w) i) = - (cos (w) - i sin (w))

= \frac{cos ( w ) + i sin ( w ) - ( cos ( w ) - i sin ( w ) )}{cos ( w ) + i sin ( w ) + cos ( w ) - i sin ( w )}

cos (w) + sin (w) i + cos (w) - i sin (w) = 2 cos (w)

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

Expand

cos (w) + sin (w) i - (cos (w) - i sin (w)) : 2 i sin (w)

= \frac{2 i sin ( w )}{2 cos ( w )}

Divide the numbers:

\frac{2}{2} = 1

= \frac{i sin ( w )}{cos ( w )}

(5 h - 3)^{2}

\frac{6 x - 18}{x ^{2} - 4} \cdot \frac{x ^{2} + 5 x + 6}{x ^{2} - 9}

- 5 + \frac{1}{3}

(3 x^{2} - 5) (3 x^{2} + 5) - x^{2} (3 x - 1)^{2}

\frac{x ^{2}}{2} + x

What is (e^{iw}-e^{-iw})/(e^{iw)+e^{-iw}} ?
The solution to (e^{iw}-e^{-iw})/(e^{iw)+e^{-iw}} is (isin(w))/(cos(w))