Question

se senx+cosx=3√3/4, o valor de sen (2x) será igual a:
gabarito:11/16

Answer 1

senx+cosx=3√3/4
(senx+cosx)²=(3√3/4)²
sen²x+2senx.cosx+cos²x = 27/16
sen²x+cos²x+2senx.cosx = 27/16
1+2senx.cosx = 27/16
2senx.cosx = 27/16 - 1
sen2x =11/16

Answer 2

sen2x = 2.senx.cosx

(senx + cosx)^2 = sen^2x + 2senx.cosx + cos^2x = 2senx.cosx + sen^2x + cos^2x = 2senx.cosx + 1 = sen2x +1

sen2x + 1 = (3rz3/4)^2
sen2x = 27/16 - 1
sen2x = 27/16 - 16/16
sen2x = 11/16