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If tan x = $\frac{4}{3}$ , 0 $^o$ < x < 90 $^o$ , fi...

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 $\frac{2}{5}$

View answer & explanation

Correct answer is B

From the diagram,

h $^2$ = 4 $^2$ + 3 $^2$ (pythagoras')

h $^2$ = 16 + 9 = 25

h = $\sqrt{25}$ = 5

Hence, sin x - cos x

= $\frac{4}{5} - \frac{3}{5}$

= $\frac{1}{5}$

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