sin x sin 80 = sin 20 sin ( 20 + x )
(1/2) [ cos ( 80 - x ) - cos ( 80 + x ) ] = (1/2) [ cos x - cos ( 40 + x ) ]
p.s. 左右方都唔明點解轉到咁...
同埋
cos ( 80 - x ) + cos ( 40 + x ) = cos x + cos ( 80 + x )
( 1/2 ) ( cos 60 ) ( cos 20 - x ) = cos x + cos ( 80 + x )
cos ( 20 - x ) - cos x = sin [ 90 - ( 80 + x ) ]
2 sin 10 sin ( 10 - x ) = sin ( 10 - x )
0 = sin ( 10 - x )
p.s. 右方我明白的 , 係唔明白左方點變 ?
係唔係有咩formula ?
有二個步驟睇唔明 , 想解一下點解會跳到個步 ?
2011-09-17 8:20 pm
回答 (3)
2011-09-17 9:13 pm
✔ 最佳答案
sinθsinα = 1/2 [ cos (θ - α) - cos (θ + α)]...........................(1) cos θ + cos α = 2 cos (θ + α)/2 cos (θ - α)/2....................(2) sin x sin 80 = sin 20 sin ( 20 + x )(1/2) [ cos ( 80 - x ) - cos ( 80 + x ) ] = (1/2) [ cos x - cos ( 40 + x ) ] by (1) cos ( 80 - x ) + cos ( 40 + x ) = cos x + cos ( 80 + x )
( 1/2 ) ( cos 60 ) ( cos 20 - x ) = cos x + cos ( 80 + x )by (2)
cos ( 20 - x ) - cos x = sin [ 90 - ( 80 + x ) ] for cos60 = 1/2, cos θ = sin(90 - θ)2 sin 10 sin ( 10 - x ) = sin ( 10 - x )
0 = sin ( 10 - x )
2011-09-17 13:50:02 補充：
cos ( 80 - x ) + cos ( 40 + x ) = cos x + cos ( 80 + x )
( 1/2 ) ( cos 60 ) ( cos 20 - x ) = cos x + cos ( 80 + x )by (2)
amendment
cos ( 80 - x ) + cos ( 40 + x ) = cos x + cos ( 80 + x )
2( cos 60 ) ( cos 20 - x ) = cos x + cos ( 80 + x ) by (2)
( cos 20 - x ) = cos x + cos ( 80 + x )
2011-09-18 3:09 am
sum-to-product and product-to-sum formulae 既中文係咩==
2011-09-17 11:43 pm
sum-to-product and product-to-sum formulae
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https://hk.answers.yahoo.com/question/index?qid=20110917000051KK00338