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Question
If 8 tan x = 15, then sin x − cos x is equal to
Options
\[\frac{8}{17}\]
\[\frac{17}{7}\]
\[\frac{1}{17}\]
\[\frac{7}{17}\]
Solution
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`
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