Question

If 16 cot x = 12, then \[\frac{\sin x - \cos x}{\sin x + \cos x}\]

Options

• \[\frac{1}{7}\]

• \[\frac{3}{7}\]

• \[\frac{2}{7}\]

• 0

Answer 1

We are given`16 cot x=12` .We are asked to find the following

`(sin x-cos x)/(sin x+cos x)`

We know that: `cot x= "Base"/"Perpendicular" `

⇒ "Base"=3

⇒ "Perpendicular"=4

⇒ `"Hypotenuse"= sqrt(("Perpendicular")^2+("Base")^2)`

⇒ `"Hypotenuse"=sqrt(16+9)`

⇒`"Hypotenuse"=5`

Now we have

`16 cot x=12`

`cot x=12/16`

`cot x=3/4`,

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

Now we find

`(Sin x- cos x)/(sin z+cos x)`

= `(4/5-3/5)/(4/5+3/5)`

=`(1/5)/(7/5)`

=`1/7`