given cot(x-y)=kcotx
prove sinx cos(x-y)=ksin(x-y)cosx
F4,,A-MATHS,,TRIGO!!,,急問喔
2007-02-28 6:00 am
回答 (2)
2007-02-28 6:08 am
✔ 最佳答案
cot(x-y)=kcotxcos(x-y)/sin(x-y)=kcosx/sinx
so cos(x-y)=kcosx--(1)
and sin(x-y)=sinx----(2)
LHS
=sinx cos(x-y)
=sin(x-y) kcosx<---put formula(1)and(2)into the originality formula..
=ksin(x-y) cosx
=RHS
so sinx cos(x-y)=ksin(x-y)cosx is ture
參考: by me ,,,, i hope i can help you~^^
2007-02-28 6:35 pm
cot(x-y)=kcotx
1/tan(x-y)=k/tanx
tanx=ktan(x-y) (By cross multipication)
sinx/cosx=ksin(x-y)/cos(x-y)
sinxcos(x-y)=ksin(x-y)cosx (By cross multipication again)
In which the identity is proven
1/tan(x-y)=k/tanx
tanx=ktan(x-y) (By cross multipication)
sinx/cosx=ksin(x-y)/cos(x-y)
sinxcos(x-y)=ksin(x-y)cosx (By cross multipication again)
In which the identity is proven
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