# If 8 tan x = 15, then sin x − cos x is equal to

Question:

If $8 \tan x=15$, then $\sin x-\cos x$ is equal to

(a) $\frac{8}{17}$

(b) $\frac{17}{7}$

(c) $\frac{1}{17}$

(d) $\frac{7}{17}$

Solution:

Given that:

$8 \tan x=15$

$\tan x=\frac{15}{8}$

$\Rightarrow$ Perpendicular $=15$

$\Rightarrow$ Base $=8$

$\Rightarrow$ Hypotenuse $=\sqrt{225+64}$

$\Rightarrow$ Hypotenuse $=17$

We know that $\sin x=\frac{\text { Perpendicular }}{\text { Hypotenuse }}$ and $\cos x=\frac{\text { Base }}{\text { Hypotenuse }}$

We find: $\sin x-\cos x$

$\Rightarrow \sin x-\cos x=\frac{15}{17}-\frac{8}{17}$

$\Rightarrow \sin x-\cos x=\frac{7}{17}$

Hence the correct option is (d)