If tan x = (frac{4}{3}), 0(^o) < x < 90(^o), find the value of sin x – cos x
-
A.
(frac{1}{10}) -
B.
(frac{1}{5}) -
C.
(frac{5}{12}) -
D.
1(frac{2}{5})
Correct Answer: Option B
Explanation
From the diagram,
h(^2) = 4(^2) + 3(^2) (pythagoras’)
h(^2) = 16 + 9 = 25
h = (sqrt{25}) = 5
Hence, sin x – cos x
= (frac{4}{5} – frac{3}{5})
= (frac{2}{5})