Тригонометрия, 11 класс. Created by vikushamur. matematika-ru

Тригонометрия, 11 класс...

vikushamur @vikushamur

July 2022 1 8 Report

Тригонометрия, 11 класс

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oganesbagoyan

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1 - sin⁶22,5° + cos⁶22,5° = 1 +(cos²22,5°)³ - (sin²22,5°)³ =
1 + ( (1 +cos2*22,5°) /2) ³ -( ( 1 -cos2*22,5°) /2 )³ =
1 + (1 /8) *( (1 +cos45°) ³ - ( 1 - cos45°) ³ ) =
1 + ( (1 /8) *(6cos45° +2cos³45°) =1 +(6*√2 / 2 +2*(√2/2)³) /8 =
1 +(6√2 /2 +√2 / 2 ) /8 =1 + 7√2 /16 = (16+ 7√2) / 16 .

*************************
cos2α = cos²α -sin²α = cos²α -(1-cos²α) =2cos²α -1⇒ cos²α =( 1+cos2α) / 2 ;
cos2α = cos²α -sin²α = 1-sin²α - sin²α = 1 -2sin²α ⇒ sin²α =( 1- cos2α) / 2.
-----
(a+b)³ -(a-b)³ =a³ +3a²b +3ab² +b³ -(a³-3a²b +3ab² -b³ ) =6a²b +2b³ ⇒
(1+b)³ -(1-b)³ =6*1² *b +2b³ =6b +2b³ * * * || a=1 ; b =cos45° ||
(1+cos45°)³ -(1-cos45°)³ =6*cos45° +2*(cos45°)³ =3√2 +√2 /2 = 7√2 / 2

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vikushamur Огромное спасибо!

oganesbagoyan рад быть полезным !

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