Question

sin75-sin15=?
la raspunsuri e radical din 2/2 dar mie imi da 2 radical din 2/2.Care este rezolvarea corecta?

Answer 1

= 2 · sin( 75 -15) /2 · cos(75 +15) /2 = 2· sin30 · cos45 = 2· 1/2 ·√2/2 = 
=√2/2

Answer 2

sin75=sin(45+30)=sin45*cos30+sin30*cos45=rad2 /2  * rad3 /2 +1/2 *rad2/2=(rad 6+rad2 ) /4

sin15=sin(45-30)=sin45*cos30-sin30*cos45=rad2 /2  * rad3 /2 -1/2 *rad2/2=(rad 6-rad2 ) /4

sin75-sin15=(rad 6+rad2 ) /4 - (rad 6-rad2 ) /4=(rad 6+rad2-rad 6+rad2 ) /4 =
2rad2/4=rad2/2