tan x = −

5

12

gives cot x =

−12

5

sec2 x = 1 + tan2 x ⇒ sec2 x = 1 +

25

144

=

169

144

⇒ sec x = ±

13

12

⇒ sec x = -

13

12

[since x lies in second quadrant]
sec x = −

13

12

gives cos x =

−12

13

, sin x = tan x × cos x
⇒ sin x = (−

5

12

) × (

−12

13

) =

5

13

, sin x =

5

13

gives cosec x =

13

5