Question

tan A/2=root over of 1-cos A÷1+cosA​

Answer 1

To prove tan a/2 =√{(1-cos a)/(1+cos a )}

RHS,

√{(1-cos a)/(1+cos a) }

=√{ (1- 1+2sin^2a/2)/(1+2cos^2a/2–1 )}

= √{2sin^2(a/2)/2cos^2(a/2)}

= √{tan^2(a/2)}

= tan a/2 = LHS (proved)

we know

cosA = 1–2sin^2(A/2)=2cos^2(A/2) -1