PROVE THAT IT IS RIGHT@@PLZ

Xxx

2011-08-14 12:53 am

PROVE THAT 2COS(180/5)=1+2SIN(180/10)

更新1:

有冇得唔用依個方法... 唶係話:用番LHS 之後用番D TRIGO RULE 變到RHS咁

更新2:

好似唔得喎就算掉轉黎睇...你個rhs變左去左邊哦度... 不如你由頭重新做多次.. 要係用 LHS=2COS(180/5) .. .. .. ..=RHS=1+2SIN(180/10) THANKS VERY MUCH

回答 (1)

用戶2053

2011-08-14 3:31 am

✔ 最佳答案

cos 54° = sin 36°4 cos³18° - 3 cos18° = 2 sin18° cos18°4 cos²18° - 3 = 2sin18° 4(1 - sin²18°) - 3 = 2sin18°4(1 - sin²18°) - 2 = 1 + 2sin18°2 - 4sin²18° = 1 + 2sin18°2 (1 - 2sin²18°) = 1 + 2sin18°2cos36° = 1 + 2sin18°2cos(180/5)° = 1 + 2sin(180/10)°

2011-08-13 23:15:17 補充：
你可以把過程倒轉來看。

2011-08-14 18:48:17 補充：
L.H.S.

= 2cos(180/5)°

= 2cos36°

= 2 (1 - 2sin²18°)

= 2 - 4sin²18°

= 2 - 4(1 - cos²18°)

= 4 cos²18° - 3 + 1

= (4 cos³18° - 3 cos18°) / cos18° + 1

= cos54° / cos18° + 1

= sin36° / cos18° + 1

= 2 sin18° cos18° / cos18° + 1

= 2 sin18° + 1

= 1 + 2sin(180/10)°

= L.H.S.

2011-08-14 18:49:03 補充：
= R.H.S.

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