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

If A+B+C=180^0 , prove that : cos^2 (A/2) + cos^2 (B/2) - cos^2 (C/2) = 2cos (A/2) cos (B/2) sin (C/2)

Prove that : 2 cos A = sqrt ([2 + sqrt (2 (1 + cos 4 A))]) , A in I or IV Quadrant.

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

In any A B C , prove that: 2{b cos^2(C/2) + c cos^2(B/2)}=a+c+b

Prove that : cos^(-1) x + cos^(-1) ((x)/(2) + (sqrt( 3-3x^2) )/( 2) ) = (pi)/ (3)

Prove that (cos C + cos A)/(c + a) + (cos B)/(b) = (1)/(b)

Prove that : cos ^(-1) ((1- a^(2))/(1+a^2)) + cos ^(-1)((1-b^(2))/(1+b^(2))) = 2 tan ^(-1) .((a+b)/(1-ab))

In any DeltaABC , prove that : (cos^2(A/2))/a + (cos^2(B/2))/b + (cos^2(C/2))/c = s^2/(abc)

(a) Prove that sin65^(@)+cos65^(@)=sqrt(2)cos 20^(@) (b) Prove that sin47^(@)+cos77^(@)=cos17^(@)

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