Posted by angel0 on Saturday, June 30, 2012 at 7:47am.
For this to be true, you must mean
tan(x/2) = tanx/(secx+1)
let Ø = x/2
then we are proving that
tanØ = tan 2Ø/(sec 2Ø + 1)
RS = (sin 2Ø/cos 2Ø)/(1/cos 2Ø + 1)
= (sin 2Ø /cos 2Ø)/( (1 + cos 2Ø)/cos 2Ø
= sin 2Ø/(1 + cos 2Ø)
= 2sinØcosØ/(1 + 2cos^2 Ø - 1)
= sinØ/cosØ
= tanØ or tan (x/2)
= LS
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