Prove that `cos(A/2)=+- sqrt((1+cosA)/2)`

Prove that cos^(-1) {sqrt((1 + x)/(2))} = (cos^(-1) x)/(2) , -1 lt x lt 1

If A=460^(@), prove that 2cos((A)/(2))=-sqrt(1+sin A)+sqrt(1-sin A)

In DeltaABC , a=3,b=4,c=2, then prove that: cosA/2 = (3sqrt(6))/(8)

Prove that ("cosec"A-cotA)^(2)=((1-cosA))/((1+cosA)).

Prove that: i) sqrt((1-cosA)/(1+cosA))="cosec"A-cotA ii) sqrt((1+sinA)/(1-sinA))=secA-tanA

Prove that cos^(-1) (sqrt(1/3))-cos^(-1) (sqrt((1)/(6)))+cos^(-1) ((sqrt(10)-1)/(3sqrt2))=cos^(-1) (2/3)

If A=340^(@), prove that 2sin((A)/(2))=-sqrt(1+sin A)+sqrt(1-sin A) and 2cos((A)/(2))=-sqrt(1+sin A)-sqrt(1-sin A)

Prove that : sqrt((1+cosA)/(1-cosA))+sqrt((1-cosA)/(1+cosA))=2 "cosec"A

Prove that: sqrt(2+sqrt(2+sqrt(2+2cos8A)))=2cosA

Prove that: cotA/2-tanA/2=(cosA/2)/(sinA/2)-(sinA/2)/(cosA/2) =(cos^(2)A/2-sin^(2)A/2)/(sinA/2cosA/2) =cosA/(1/2.(2sinA/2cosA/2)) =(2cosA)/(sinA)=2cotA = RHS. Hence Proved.