Question

Alguém me ajuda?

Ajude uma pessoa de humanas. ❤

Answer 1

Olá,

cos(x) = 1/3

sen²(x) + cos²(x) = 1
sen²(x) = 1-cos²(x)
sen²(x) = 1-(1/3)²
sen²(x) = 1-1²/3²
sen²(x) = 1-1/9
sen²(x) = (9-1)/9
sen²(x) = 8/9
sen(x) = √8/9
sen(x) = √8/√9 
sen(x) = 2√2/3

cossec(x) = 1/sen(x) = 1/(2√2/3) = (1/1)/(2√2/3) = 3/2√2 
cossec(x) = 3/2√2 · √2/√2 = (3√2)/4

sec(x) = 1/cos(x) = 1/(1/3) = (1/1)/(1/3) = 3

cotg(x) = 1/tg(x) = 1/sen(x)/cos(x) = (1/1)/(sen(x)/cos(x))
cotg(x) = cos(x)/sen(x) = (1/3)/(2√2/3) = 1/3 · 3/2√2
cotg(x) = 3/6√2 = 1/2√2 = 1/2√2 ·√2/√2 = √2/4

cossec(x) - sec(x) = 3√2/4 - 3 = (3√2-12)/4
cotg(x) - 1 = √2/4 - 1 = (√2-4)/4

y = ((3√2-12)/4)/((√2-4)/4)
y = (3√2-12)/4 · 4/(√2-4)
y = 4(3√2-12)/4(√2-4)
y = (3√2-12)/(√2-4)
y = 3(√2-4)/(√2-4)
y = 3

Resposta:

y = 3