Question

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

Options

• \[\frac{8}{17}\]

• \[\frac{17}{7}\]

• \[\frac{1}{17}\]

• \[\frac{7}{17}\]

Answer 1

Given that:

`8 tan x=15`

`tan x=15/8` 

⇒` "Perpendicular"=15`

⇒` "Base"=8` 

⇒` "Hypotenuse"=sqrt225+64`

⇒ `"Hypotenuse"=17`

We know that `sin x = "Perpendicular"/"Hypotenuse" and cos x = "Base"/"Hypotenuse"` 

We find: `sin x-cos x` 

⇒` sin x-cos x= 15/17-8/17` 

⇒` sin x-cos x = 7/17`