Question

Синус 75= Косинус 105= Тангенс 15=

Answer 1

$sin75 = sin(45+30)=sin45*cos30+cos45*sin30 = \frac{ \sqrt{2} }{2}* \frac{ \sqrt{3} }{2}+$$\frac{ \sqrt{2} }{2}* \frac{1}{2}= \frac{ \sqrt{6} }{4}+ \frac{ \sqrt{2} }{4}= \frac{ \sqrt{6}+ \sqrt{2} }{4}$
$cos105 = cos(60+45) = cos60*cos45-sin60*sin45 =$ $\frac{1}{2}* \frac{ \sqrt{2} }{2}- \frac{ \sqrt{3} }{2}* \frac{ \sqrt{2} }{2}= \frac{ \sqrt{2} }{4}- \frac{ \sqrt{6} }{4}= \frac{ \sqrt{2}- \sqrt{6} }{4}$
$tg15 = tg (45 - 30) = \frac{tg45-tg30}{1+tg45*tg30}= \frac{1- \frac{1}{ \sqrt{3} } }{1+1* \frac{1}{ \sqrt{3} } }=$ $\frac{1- \frac{1}{ \sqrt{3} } }{1+ \frac{1}{ \sqrt{3 } } }= \frac{(1- \frac{1}{ \sqrt{3} })^2 }{1- \frac{1}{3} }=$ $\frac{ \frac{4}{3}- \frac{2}{ \sqrt{3} } }{ \frac{2}{3} }=2- \frac{3}{ \sqrt{3} }=2- \sqrt{3}$