diketahui [tex] \sin(x) \cos(x) = \frac{12}{49} [/tex] nilai [tex] \frac{1}{ \cos(x) } - \frac{1}{ \sin(x) } [/tex]

[tex]\dfrac{1}{\cos x}-\dfrac{1}{\sin x}&=\dfrac{\sin x - \cos x}{\cos x\sin x}[/tex]

Nilai penyebut sudah diketahui 12/49
Mencari nilai pembilang, misalkan sin x - cos x = p, kuadratkan kedua ruas

[tex]\begin{aligned} (\sin x-\cos x)^2&=p^2\\ (\sin^2 x+\cos^2 x)-2\sin x\cos\x &=p^2\\ 1-2\left(\dfrac{12}{49}\right)&=p^2\rightarrow p =\dfrac{5}{7} \end{aligned}[/tex]

jadi 

[tex]\dfrac{1}{\cos x}-\dfrac{1}{\sin x}=\dfrac{\frac{5}{7}}{\frac{12}{49}}=\dfrac{35}{12}[/tex]