Question

cos^2(x/2)-sin^2(x/2)

2sin(x/2)cos(x/2)

Answer 1

sin ^ 2 ( x ) + cos ^ 2 ( x ) = 1

sin ^ 2 ( x ) = 1 - cos ^ 2 ( x )

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

cos ^ 2 ( x / 2 ) - sin ^ 2 ( x / 2 ) =

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

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

2 cos ^ 2 ( x / 2 ) - 1

cos ^ 2 ( x / 2 ) = [ 1 + cos ( x ) ] / 2

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

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

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

cos ^ 2 ( x / 2 ) - sin ^ 2 ( x / 2 ) = cos ( x )

2 sin ( x ) cos ( x ) = sin ( 2 x )

2 sin( x / 2 ) cos ( x /2 ) = sin ( 2 * x / 2 ) = sin ( x )

2 sin ( x / 2 ) cos ( x / 2 ) = sin ( x )