Find the exact values of the sine, cosine, and tangent of the angle. 255=300-45

Sin 255 = sin (300 - 45) = sin 300 cos 45 - cos 300 sin 45; where sin 300 = - sin (360 - 60) = - sin 60 = - √3/2, sin 45 = cos 45 = 1/√2, cos 300 = cos (360 - 60) = cos 60 = 1/2

Therefore, sin 255 = (-√3/2) (1/√2) - (1/2) (1/√2) = - √3/2√2 - 1/2√2 = - (√3 + 1) / 2√2 = - (√6 + √2) / 4

cos 255 = cos (300 - 45) = cos 300 cos 45 + sin 300 sin 45 = (1/2) (1/√2) + (-√3/2) (1/√2) = (1 - √3) / 2√2 = (√2 - √6) / 4

tan 255 = tan (300 - 45) = (tan 300 - tan 45) / (1 + tan 300 tan 45); where tan 300 = sin 300 / cos 300 = (-√3/2) / (1/2) = - √3 and tan 45 = 1

Therefore, tan 255 = (-√3 - 1) / (1 + (-√3)) = (-√3 - 1) / (1 - √3) = √3 + 2