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)