How do you verify $(2tan(x/2)) / (1+tan^2(x/2)) = sin x$ ?

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Answer 1 · 2018-03-09T19:54:53

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$LHS : (2tan(x/2))/(1+tan^2(x/2))$

$=((2sin(x/2))/cos(x/2))/sec^2(x/2)$ -> use the property $1+tan^2x=sec^2x$

$=((2sin(x/2))/cos(x/2))/(1/cos ^2(x/2))$

$=(2sin(x/2))/cos(x/2) * cos ^2(x/2)/1$

$=(2sin(x/2))/cancelcos(x/2) * cos ^cancel2(x/2)/1$

$=2sin(x/2)cos(x/2)$

$=sin2(x/2)$ ->use the property $sin2x=2sinxcosx$

$=sincancel2(x/cancel2)$

$=sinx$

$=RHS$

How do you verify (2tan(x/2)) / (1+tan^2(x/2)) = sin x(2tan(x/2)) / (1+tan^2(x/2)) = sin x?