If sin x = (frac{5}{13}) and 0o (leq) x (leq) 90o, find the value of (cos x – tan x)
-
A.
(frac{7}{13}) -
B.
(frac{12}{13}) -
C.
(frac{79}{156}) -
D.
(frac{209}{156})
Correct Answer: Option C
Explanation
Sin x = (frac{5}{13})
0o (leq) x (leq) 90o, (cos x – tan x)
AC2 = AB2 + BC2
132 = 52 + BC2
169 – 25 + BC2
169 – 25 = BC2
144 = BC2
Cos x = (frac{Adj}{Hyp}) = (frac{12}{13})
BC = (sqrt{144})
BC = 12
tan x = (frac{opp}{adj} = frac{5}{12})
BC = 12
cos x – tan x = (frac{12}{13} – frac{5}{12})
(frac{144 – 65}{156} = frac{79}{156})