Given as
sin x = 12/13 and x lies in the second quadrant.
As we know, in second quadrant, sin x and cosec x are positive and all other ratios are negative.
On using the formulas,
cos x = √(1 - sin2 x)
= – √(1 - (12/13)2)
= – √(1 - (144/169))
= – √(169 - 144)/169
= -√(25/169)
= – 5/13
As we know,
tan x = sin x/cos x
sec x = 1/cos x
Then,
tan x = (12/13)/(-5/13)
= -12/5
sec x = 1/(-5/13)
= -13/5
sec x + tan x = -13/5 + (-12/5)
= (-13 - 12)/5
= -25/5
= -5
Thus, sec x + tan x = -5
