Prove that `cos(B/2)=sqrt((1+cosB)/2)`

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

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

In any DeltaABC , prove that (cos2A)/a^(2)-(cos2B)/b^(2)=(1/a^(2)-1/b^(2))

Prove that ((1-cosB)(1+cosB))/((1-sinB)(1+sinB))=1/3 when B=30^@

int_(0)^( Prove that )sqrt(1+cos2x)dx=22sqrt(2)-sqrt((3)/(2))

In DeltaABC , prove that: sin(A+B/2).cosB/2=(c+a)/(a+b)cosC/2.cos(A-B)/(2)

prove that cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))=2cos^(-1)sqrt((1+x)/(2))

If tan A tan B=sqrt((a-b)/(a+b)), prove that (a-b cos2A)(a-b cos2B)=a^(2)-b^(2)

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)

If pi