1)sin^4альфа +cos^4альфа 2)sin^6 альфа +-cos^6 альфа. Created by 1Tobi. algebra-ru

1)sin^4альфа +cos^4альфа 2)sin^6 альфа +-cos^6 альфа...

1Tobi @1Tobi

July 2022 1 15 Report

1)sin^4альфа +cos^4альфа
2)sin^6 альфа +-cos^6 альфа

Answers & Comments

NNNLLL54

Verified answer

Ответ:

$1)\ \ sin^4a+cos^4a=(sin^4a+2\cdot sin^2a\cdot cos^2a+cos^4a)-2\cdot sin^2a\cdot cos^2a=\\\\=(\underbrace{sin^2a+cos^2a}_{1})^2-2\cdot sin^2a\cdot cos^2a=1-2\cdot (sina\cdot cosa)^2=\\\\=1-2\cdot \Big(\dfrac{1}{2}\cdot sin2a\Big)^2=1-\dfrac{1}{2}\cdot sin^22a$

$2)\ \ sin^6a+cos^6a=(sin^2a)^3+(cos^2a)^3=\\\\=(\underbrace{sin^2a+cos^2a}_{1})(sin^4a-sin^2a\cdot cos^2a+cos^4a)=\\\\=(sin^4a+cos^4a)-sin^2a\cdot cos^2a=\Big(1-\dfrac{1}{2}\cdot sin^22a\Big)-(sina\cdot cosa)^2=\\\\=\Big(1-\dfrac{1}{2}\cdot sin^22a\Big)-\Big(\dfrac{1}{2}\cdot sin2a\Big)^2=1-\dfrac{1}{2}\cdot sin^22a-\dfrac{1}{4}\cdot sin^22a=\\\\=1-\dfrac{3}{4}\cdot sin^22a$

$3)\ \ sin^6a-cos^6a=(sin^2a)^3-(cos^2a)^3=\\\\=(\underbrace{sin^2a-cos^2a}_{-cos2a})(sin^4a+sin^2a\cdot cos^2a+cos^4a)=\\\\=-cos2a\cdot \Big((sin^4a+cos^4a)+sin^2a\cdot cos^2a\Big)=\\\\=-cos2a\cdot \Big(\Big(1-\dfrac{1}{2}\cdot sin^22a\Big)+(sina\cdot cosa)^2\Big)=\\\\=-cos2a\cdot \Big(\Big(1-\dfrac{1}{2}\cdot sin^22a\Big)+\Big(\dfrac{1}{2}\cdot sin2a\Big)^2\Big)=\\\\=-cos2a\cdot \Big(1-\dfrac{1}{2}\cdot sin^22a+\dfrac{1}{4}\cdot sin^22a\Big)=\\\\=cos2a\cdot \Big(\dfrac{1}{4}\cdot sin^22a-1\Big)$

Формулы:

$sin2a=2\, sina\cdot cosa\\\\cos2a=cos^2a-sin^2a\\\\a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)$

2 votes Thanks 1

Answers & Comments

Verified answer

2 4 8 10 11 16 18

pomogite ochen srochno dayu 100 balov 1sinalfa cosalfa2sinalfa cosalfa3sin

pomogite pozhalujsta v cehe predpriyatiya rabotayut 15 chelovek iz nih 6 chelovek i

pomogite pozhalujsta y2x x y 60

znajdit pririst funkciyi u yaksho h01 h 01 i y x2 1

pomogite pozhalujsta nuzhno ochen srochno reshit

рекомендуемые вопросы

Helpful Links

Helpful Social