Verified answer

cos(75) = sen(90 - 75) = sen(15)

sen(15) = sen(45 - 30)

sen(a - b) = sen(a)*cos(b) - cos(a)*sen(b)

sen(45 - 30) = sen(45)*cos(30) - cos(45)*sen(30)

sen(15) = √2/2*√3/2 - √2/2*1/2 = (√6 - √2)/4

sen(105) = sen(60 + 45)

sen(60 + 45) = sen(60)*cos(45) + cos(60)*sen(45)

sen(105) = √3/2*√2/2 + 1/2*√2/2 = (√6 + √2)/4

sen(105) - cos(75) = (√6 + √2)/4 - (√6 - √2)/4 = 2√2/4 = √2/2

pronto