How do you verify the identity #tan(A/2)=sinA/(1+cosA)#?

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Answer 1 · 2016-12-14T17:43:42

See verification below

We use

#sin2theta=2sintheta costheta#

and #cos2theta=2cos^2theta-1#

We deduce,

#sinA=2sin(A/2)cos(A/2)#

and, #cosA=2cos^2(A/2)-1#

#:. R.H.S=sinA/(1+cosA)=(2sin(A/2)cos(A/2))/(1+2cos^2(A/2)-1)#

#=(2sin(A/2)cos(A/2))/(2cos^2(A/2))=sin(A/2)/cos(A/2)#

#=tan(A/2)=LHS#

Q. E.D