Question

Calcule cos x, sabendo que 5 sec x - 3 tan ao quadrado de x = 1.​

Answer 1

sec ² x = 1 + tan ² x

⇒ tan ² x = sec ² x - 1

...

5 sec x - 3 tan ² x = 1

5 sec x = 1 + 3 tan ² x

5 sec x = 1 + 3. (sec ² x -1)

5 sec x = 1 + 3sec ² x -3

0 = 3 sec ² x - 5 sec x -2

Δ = -5 ² -4.3.-2

Δ = 25 +24 = 49

sec x = (5 ± 7)/2.3

sec x ‘ = 12/6 = 2

sec x “ = -2/6 = -1/3

...

sec x = 1/ cos x

2 = 1/ cos x

cos x = 1/2

ou

-1/3 = 1/cos x

cos x = -3 {∉}

S = { cos x = 1/2 | x = π/3 }