How is (cosa + i sina -1)/(cosa +i sina +1) = 2i tan a/2..??! Please explain....

Dear Student,
Please find below the solution to the asked query:

R.H.S. looks incorrect. It should be i tana2L.H.S.=cosa+i sina-1cosa+i sina+1=cosa-1+i sinacosa+1+i sina=1-2sin2a2-1+i 2sina2cosa22cos2a2-1+1+i2sina2cosa2=-2sin2a2+i 2sina2cosa22cos2a2+i2sina2cosa2=-2sina22cosa2sina2-icosa2cosa2+isina2=1i-tana2isina2-i2cosa2cosa2+isina2=-i-tana2isina2+cosa2cosa2+isina2 As 1i=-i and i2=-1=itana2cosa2+isina2cosa2+isina2=itana2=R.H.S.

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