sin,cos Difficult

L.H.S. = 2 sin^2 ( x / 2 )

R.H.S. = 1 - cos x

= 1 - cos ( x /2 + x / 2 )

= 1 - [ cos (x / 2) cos (x / 2 )- sin (x / 2) sin( x /2) ]

[ As cos ( A + B ) = cosAcosB - sinAsinB]

= 1 - [ cos^2 ( x / 2 ) - sin^2 ( x / 2 )]

= 1 - [ 1 - sin^2 ( x / 2 ) - sin^2 ( x / 2 )]

[ As sin^2 A + cos^2 A = 1]

= 1 - 1 + 2 sin^2 ( x / 2 )

= 2 sin^2 ( x / 2 )

= R.H.S.

cos (x) = cos (x/2) cos (x/2) - sin (x/2) sin (x/2)
cos x = [cos (x/2)]^2 - [sin (x/2)]^2
cos x = 1 - 2 [sin (x/2)]^2
2 [sin (x/2)]^2 = 1 - cos x