Asked by James
cos^2(x/2)-sin^2(x/2)
2sin(x/2)cos(x/2)
2sin(x/2)cos(x/2)
Answers
Answered by
Bosnian
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 )
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 )
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