Reduce complex exponential expression

[kususe]

Homework Statement

prove that:
1-exp(-iwt)= 2i*sin(wt/2)

Homework Equations

exp(iwt)= cos (wt) + i*sin(wt)

The Attempt at a Solution

I attempted to express the exponential into sum of cos and sin and considering t=2*t/2 in order to obtain an argument like (t/2) (using duplication expression of trigonometry theory).


Thanks in advance

 

[phyzguy]

You must have the problem wrong, because the equation you are trying to prove is not true. For example, if wt = pi/2, then the left-hand side is equal to 1+i and the right-hand side is equal to √2 * i.

 

[kususe]

Yes, you're right and the problem was wrong.
In the right-hand side of first expression, there's also

exp(-iwt/2)

And the equivalence is proved.