Given cosec x = 13/5, x being the angle.
cosec x = 1 / Sin x => sin x = 1 / cosec x => sin x = 1 / (13/5) => sin x = 5/13
So in a right angled triangle sin x = perpendicular height(h) / l, l being the side opposite to right angle.
So h = 5, l = 13.
From Pythagoras theorem l^2 = h^2 + b^2, b is the base
13^2 = 5^2 + b^2 => b^2 = 13^2 - 5^2 => b^2 = 169 - 25 => b^2 = 144 => b= 12
sin x = 5/13
cos x = b / l = 12/13
sec x = 1/cos x = 1/ (12/13) = 13/12
tan x = sin x / cos x = (5/13) / (12/13) = 5/12
