Question

simplyfy sin100°+cos100°

Answer 1

sin 100 degree = sin ( 90degree + 10 degree)
= cos 10 degree
cos 100 degree + cos 10 degree
= 2 cos {( 100 + 10 )degree / 2}* cos {( 100 - 10) degree / 2}
= 2 cos 55 degree * cos 45 degree
= 2 cos 55 degree * 1 / root 2
=root 2 cos 55 degree

Answer 2

sin100°=sin(90+10)°=cos10°
sin100°+cos100°=cos10°+cos100°
=2cos(100+10/2)°×cos(100-10/4)°
=2cos55°×cos45°
=2Cos55°×1/√2
=√2cos55°