Question

sin52+sin90+sin142+sin232+sin322=???

Answer 1

2*sin(52+142)/2 * cos(142-52)/2  + 1+ 2*sin(232+322)/2*cos(322-232)/2=
2*sin(97)*cos(45)+1+2*sin(277)*cos(45)=$sqrt{2}$(sin97+sin277)+1=
$sqrt{2}$(sin97+sin(180+97))+1=$sqrt{2}$(sin97-sin(97))+1=1