Find the exact value of sin(75°). Give your answer in its simplest form.
sin(A+B) ≡ sin(A)cos(B) + sin(B)cos(A)
⇒ sin(75°) = sin(30+45)° = sin(30°)cos(45°) + sin(45°)cos(30°)
= ½ × 1/√2 + 1/√2 ×(√3)/2 = 1/(2√2) + (√3)/(2√2)
= (1+√3)/(2√2)
sin(A+B) ≡ sin(A)cos(B) + sin(B)cos(A)
⇒ sin(75°) = sin(30+45)° = sin(30°)cos(45°) + sin(45°)cos(30°)
= ½ × 1/√2 + 1/√2 ×(√3)/2 = 1/(2√2) + (√3)/(2√2)
= (1+√3)/(2√2)
