Sin75cos75tg75= решите

Question

Sin75cos75tg75= решите

Answer 1

1/2*sin150*tg75=1/2*sin30*tg75=1/4*tg75=1/4*tg(45+30)=
=1/4*(tg45+tg30)/(1-tg75*tg30)=1/4*(1+1/√3)/(1-1/√3)=
=1/4*(√3+1)²/(√3-1)(√3+1)=1/4*(3+2√3+1)/(3-1)=1/4*(4+2√3)/2=
=1/4*2(2+√3)/2=(2+√3)/4