Question

помогите плиззз sin75 и cos 75,заменяя на 45+30; sin15 и cos15,заменяя на 45-30

Answer 1

1)$sin75 = sin(45+30) = sin45cdot cos30+sin30cdot cos45$

$=frac {sqrt 2} {2} cdot frac{sqrt 3}{2} + frac {1} {2} cdot frac {sqrt2}{2}$

$=frac{sqrt6}{4}+frac {sqrt2}{4} = frac {sqrt6 +sqrt2}{4}$

 

2)$cos75 = cos(45+30) = cos45cdot cos30 - sin45 cdot sin30$

$= frac {sqrt2}{2} cdot frac{sqrt 3 }{2} - frac{sqrt2}{2} cdot frac{1}{2}$

$=frac{sqrt6}{4}- frac {sqrt2}{4} = frac{sqrt6 - sqrt2}{4}$

 

3)$sin15 = sin(45-30) = sin45cdot cos30-sin30cdot cos45$

$=frac {sqrt 2} {2} cdot frac{sqrt 3}{2} - frac {1} {2} cdot frac {sqrt2}{2}$

$=frac{sqrt6}{4}-frac {sqrt2}{4} = frac {sqrt6 -sqrt2}{4}$

 

 

4) $cos15 = cos(45-30) = cos45cdot cos30 + sin45 cdot sin30$

$= frac {sqrt2}{2} cdot frac{sqrt 3 }{2} + frac{sqrt2}{2} cdot frac{1}{2}$

$=frac{sqrt6}{4}+ frac {sqrt2}{4} = frac{sqrt6 + sqrt2}{4}$