a triangle ABC, how to prove sin^2(A)-sin^2(B)=sin(A-B)sinC?
回答 (4)
2020-12-03 5:28 pm
✔ 最佳答案
sin(A-B)sinC=sin(A-B)sin(A+B)=(sinAcosB-cosAsinB)(sinAcosB+cosAsinB)=sin^2Acos^2B-cos^2Asin^2B=sin^2Acos^2B-(1-sin^2A)(1-cos^2B)
=sin^2Acos^2B-(1-sin^2A-cos^2B+sin^2Acos^2B)
= -1+sin^2A+cos^2B= -1+sin^2A+(1-sin^2B)=sin^2A-sin^2B
硬要從左到右需要不少技巧,需加上一些臨時輔佐數字,例如:加1再減1..等等,不是一時想得到的,若是規定如此只好請你將我寫得從右寫到左,至於其他方法目前還沒想到
2020-12-06 7:01 pm
LHS--->RHS:-
We are learning -0 to +0 and +0 to -0,properly,
For the -0 to +0 refers to +sinC
For the +0 to -0 refers to +sinC
;
Both improperly !?
Yet properly to sinC.
We are learning -0 to +0 and +0 to -0,properly,
For the -0 to +0 refers to +sinC
For the +0 to -0 refers to +sinC
;
Both improperly !?
Yet properly to sinC.
2020-12-04 5:37 am
由要證明的等式 sin^2(A)-sin^2(B)=sin(A-B)sinC
來看, 顯然是從右式變到左式比較自然. 也沒有規
定一定要從左式變到右式才正規. 若一定要, 那麼
把右式變成左式的過程反著寫就可以了.
來看, 顯然是從右式變到左式比較自然. 也沒有規
定一定要從左式變到右式才正規. 若一定要, 那麼
把右式變成左式的過程反著寫就可以了.
2020-12-03 5:56 pm
Gong, can you rewrite LHS instead of RHS?
收錄日期: 2021-04-11 23:24:24
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https://hk.answers.yahoo.com/question/index?qid=20201203070729AA8mEkS