Question

prough that tan A/2=(√1-cos a/1+cos a​)​

Answer 1

Step-by-step explanation:

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 (hence proved)

Note:

cosA = 1–2sin^2(A/2)=2cos^2(A/2) -1