Question

determine o valor numerico da expressão: (sen2x-cos3x) / (tg(x/2)+cotgx) para x = pi/3

Answer 1

(sen 2x - cos 3x)/(tg x/2 + cotg x)      x = π/3

{sen 2(π/3) - cos 3(π/3)}/{tg (π/3)/2 + 1/tg(π/3)/2}

(sen 120° - cos 180°)/( tg 30° + 1/tg 30°)

{(√3/2 - (-1)}/(√3/3 + 1/√3/3)

(√3/2 + 1)/(√3/3 + 1/3√3)

(√3 + 2/2)/(9 + 1/3√3)

(√3 + 2/2)/(10/3√3) = √3 + 2/2 . 3√3/10 = 7√3/20