Question

Sin75 и cos 75,заменяя на 45+30; sin15 и cos15,заменяя на 45-30

Answer 1

1)$sin75 = sin(45+30) = sin45\cdot cos30+sin30\cdot cos45$

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

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

2)$cos75 = cos(45+30) = cos45\cdot cos30 - sin45 \cdot sin30$

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

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

3)$sin15 = sin(45-30) = sin45\cdot cos30-sin30\cdot cos45$

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

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

4) $cos15 = cos(45-30) = cos45\cdot cos30 + sin45 \cdot sin30$

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

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