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प्रश्न
If 16 cot x = 12, then \[\frac{\sin x - \cos x}{\sin x + \cos x}\]
विकल्प
\[\frac{1}{7}\]
\[\frac{3}{7}\]
\[\frac{2}{7}\]
0
उत्तर
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`
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