可怜的孩子!你应该加括号的.
是 cos θ -cos φ = -2 sin [ (θ+φ)/2 ] sin [ (θ-φ)/2 ]
= = = = = = = = =
令 x =(θ+φ)/2,
y = (θ-φ)/2,
则 θ =x +y,
φ =x -y.
所以 cos θ =cos (x +y)
=cos x cos y -sin x sin y,
cos φ =cos (x -y)
=cos x cos y +sin x sin y.
所以 cos θ -cos φ = -2 sin x sin y
= -2 sin [ (θ+φ)/2 ] sin [ (θ-φ)/2 ].
= = = = = = = = =
1.换元法.
2.和差化积.
3.这题说明了,和差化积公式可以用基本的和角公式以及差角公式来推导.