Question -
Answer -
Given:
Sin x = 12/13 and x lies in the second quadrant.
We know, in second quadrant, sin x and cosec x arepositive and all other ratios are negative.
By using the formulas,
Cos x = √(1-sin2 x)
= – √(1-(12/13)2)
= – √(1- (144/169))
= – √(169-144)/169
= -√(25/169)
= – 5/13
We know,
tan x = sin x/cos x
sec x = 1/cos x
Now,
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
∴ Sec x + tan x = -5