If $a = \cos{ heta + i\sin{ heta,\ then\ \frac{1 + a}{1 - a}}}$ is equal to

Question

If $a = \cos{	heta + i\sin{	heta,\ then\ \frac{1 + a}{1 - a}}}$ is equal to

Dr. Abubacker · Accepted Answer

(c)
$\frac{1 + a}{1 - a} = \frac{e^{\frac{- i	heta}{2}}(1 + e^{i	heta})}{e^{\frac{- i	heta}{2}}(1 - e^{i	heta})} = \frac{e^{- i\left( \frac{	heta}{2} ight)} + e^{i\frac{	heta}{2}}}{e^{- i\left( \frac{	heta}{2} ight)} - e^{- i\frac{	heta}{2}}}$
$= \ \frac{2\cos\frac{	heta}{2}}{- 2i\sin\frac{	heta}{2}} = i\cot\frac{	heta}{2}$

Q. If $a = \cos{\theta + i\sin{\theta,\ then\ \frac{1 + a}{1 - a}}}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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