Question

exact value using sum or difference identity ;
sin255 degrees

Answer 1

Look for a combination of "exact value" angles that gives you 255...

how about 120 + 135

so now sin (255) = sin (120 + 135)=
sin 120 cos 135 + cos 120 sin 135 =
(sqrt3/2)(-sqrt2/2) + (-1/2)(sqrt2/2) =
-sqrt6/4 - sqrt2/4 =
-(sqrt6 + sqrt2)/4

or, rearranging to match your choices:
(-sqrt2 - sqrt6)/4 (a)

Answer 2

this is really the sum of 120 degrees and 135

so you would have

sin(120 + 135) = sin(120)cos(135) - cos(120)sin(135)

both angles have exact values....

Answer 3

Thank you so much!!!!