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

Prove that ( sin 2 A )/( 1 - cos 2 A) = cot A

Prove that : (1+sin 2A)/(cos 2A) = (cos A + sin A)/(cos A - sin A) = tan (pi/4 + A)

Prove that : (tan A + (1)/ (cos A))^(2) + (tan A - (1)/ (cos A))^(2) = 2 ((1 + sin^(2) A)/ (1 - sin^(2) A))

Prove that : (sin A)/ (1 + cos A) + (1 + cos A)/ (sin A) = 2 cosec A

Prove that (sin 2 A )/(1- cos 2 A ) . (1- cos A )/( cos A ) = tan ""(A)/(2)

Prove that : (1)/ (sin A - cos A) - (1)/ (sin A + cos A) = (2 cos A)/(2 sin^(2) A - 1)

Prove that : (1+sin 2A-cos 2A)/(1+sin 2A+cos 2A) = tan A

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

Prove that : int_0^(pi/2)sqrt(1-sin2x)dx=2(sqrt(2)-1)

prove that (sin2A)/(1-cos2A)=cotA