tan³ 75 + tan³ 15 = ?

jawab

tan 75= tan (45+30) = 2+ √3
tan 15 = tan(45-30) =  2 - √3

tan 75 = a = 2+ √3
tan 15 = b = 2 - √3
a + b= 4
a, b =  1

tan³ 75 + tan³ 15 =  a³ + b³

a³ + b³ = ( a + b)³ - 3(ab)(a + b)
tan³ 75 + tan³ 15 = (2)³ - 3(1)(4)
tan³ 75 + tan³ 15 = 8 -12
tan³ 75 + tan³ 15 = - 4