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if `a = costheta +i sin theta `, prove that `(1+a)/(1-a) = cot(theta/2)i`

Answer» `(1+a)/(1-a)=((1+cos theta)+ i sin theta)/((1-cos theta)- i sin theta)xx((1-cos theta)+ i sin theta)/((1-cos theta)+ i sin theta)`
`=((1-cos^(2)theta-sin^(2)theta)+2 i sin theta)/((1-cos theta)^(2)+ sin^(2) theta)=(1-(cos^(2)theta+sin^(2)theta)+2 i sin theta)/(1+(cos^(2)theta+sin^(2)theta)-2 cos theta)`
`=(2 i sin theta)/(2(1-cos theta))=(i sin theta)/((1-cos theta))=(2 sin (theta//2)cos (theta//2))/(2 sin^(2)(theta//2)).i = ("cot"(theta)/(2))i`.


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