Question

slove the equation cos2A =√5+1/4 A belong to 0,2π

Answer 1

cos2A = ( √5 + 1)/4

we know,
( √5 + 1)/4 = cos36° = cosπ/5

cos2A = cosπ/5
2A = 2nπ ± π/5
A = nπ ± π/10

A = π/10 , 11π/10 , in [ 0, 2π ]
hence, two values of A in [ 0, 2π ]

and value of 2A in [ 0, 2π ] is only one