Question

13- Sabendo que cos x = 1/2 , calcule o valor da expressão E= cotg²x-1 / cossec² x+sec x.

Answer 1

Resposta:

= - 1/5

Explicação passo-a-passo:

cos x = 1/2 , calcule o valor da expressão E= (cotg²x-1) / (cossec² x+sec x)

Cos x = 1/2

sen^2 x + cos^2 x = 1

sen^2 x + (1/2)^2 = 1

sen^2 x + 1/4 = 1

sen^2 x = 1 - 1/4

sen^2 x = (4-1)/4

sen^2 x = 3/4

sen x = √(3/4)

sen x = √3/2

Cos x = 1/2

E= (cotg²x-1) / (cossec² x+sec x)

cotg x = cos x/sen x

Cotg x = 1/2 : √3/2

Cotg x = 1/2 . 2/√3

Cotg x = 2/2 . 1/√3

Cotg x = 1/√3 . √3/√3

Cotg x = √3/3

Cossec x = 1/sen x

Cossec x = 1 :√3/2

Cossec x = 2/√3 . √3/√3

Cossec x = 2√3/3

Sec x = 1/cos x

Sec x = 1 : 1/2

Sec x = 1.2

Sec x = 2

E= (cotg²x-1) / (cossec² x+sec x)

E=[(√3/3)^2 - 1]/[(2√3/3)^2 + 2]

E = [A]/[B]

[A]

= (√3/3)^2 - 1

= 3/9 (:3)/(:3) - 1

= 1/3 - 1

= 1/3 - 3/3

= - 2/3

[B]

= (2√3/3)^2 + 2

= (4.3/9) + 2

= 12/9 (:3)/(:3) + 2

= 4/3 + 2

= (4+3.2)/3

= (4+6)/3

= 10/3

= A/B

= - 2/3 : 10/3

= - 2/3 . 3/10

= - 3/3 . 2/10 (:2)/(:2)

= - 1/5

R.: - 1/5