Trig, half angle identity?

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Trig, half angle identity?

Prove that:

tanX/2 equals to cscX - cotX

2007-10-12 17:28:37 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics

2 answers

tanX/2
= sinX/2 / cosX/2
= 2sin^2(X/2) / sinX, multiplied by 2sinX/2 / (2sinX/2)
= (1-cosX)/sinX
= 1/sinX - cosX/sinX
= cscX - cotX

2007-10-12 17:37:22 · answer #1 · answered by sahsjing 7 · 0⤊ 0⤋

i found a formula for tan^2 x/2 = (1-cosx)/(1+cosx)

(1-cosx)(1-cosx)/(1+cosx)(1-cosx)
=(1-cosx)^2/(1-cos^2x)
=(1-cosx)^2/ sin^2x

tan x/2 = sqrt((1-cosx)^2/sin^2x)
= (1-cosx)/sinx
= csc x - cot x

2007-10-12 17:42:03 · answer #2 · answered by norman 7 · 0⤊ 0⤋