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 is C

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 = \(\frac{12}{13} - \frac{5}{12}\)

\(\frac{144 - 65}{156} = \frac{79}{156}\)