Question

calcule o valor de tg pi/3 - cotg pi/6 + sec pi/6 - cosec pi/3

Answer 1

pi/3 = 180°/3 = 60°
=> tg pi/3 = tg 60° = raiz de 3

pi/6 = 180°/6 = 30° =>
cotg pi/6 =
= 1/(tg pi/6) =
= 1/(tg 30°) =
= 1/(rai de 3 / 3) =
= 3 / raiz de 3 =
= raiz de 3

sec pi/6 =
= 1/(cos pi/6) =
= 1/(cos 30°) =
= 1/(raiz de 3 / 3 =
3 / raiz de 3 =
= raiz de 3

Cosec pi/3 =
= 1/(sen pi/3) =
= 1/(sen 60°) =
= 1/(raiz de 3 / 3 =
= 3/ raiz de 3 =
= raiz de 3

Logo:
tg pi/3 - cotg pi/6 + sec pi/6 - cossec pi/3 =
= (raiz de 3) - (raiz de 3) + (raiz de 3) - (raiz de 3) =
= 0

Resposta: 0