Question

dado cossec x = raiz de 3 , calcule sec x = ?

Answer 1

cossec x = 1/sen x
√3 = 1/sen x
sen x = 1 / √3
sen x = √3 / 3

sec = 1 / cos x
temos que:
 
sen²x + cos²x = 1
(√3 / 3)² + cos²x = 1
3/9  + cos²x = 1
          cos²x = 1 - 3/9
          cos²x = 1 - 1/3
          cos²x = 2/3
          cos x = √2/√3
          cos x =  √2 . √3  / 3
          cos x = √6 /3

como a sec x = 1/cos x

sec x = 1/ √6/3
sec x = 1 . 3  /√6
sec x = 3 . √6  / 6
sec x = √6 / 2