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प्रश्न
If 3 cot θ = 4, find the value of \[\frac{4 \cos \theta - \sin \theta}{2 \cos \theta + \sin \theta}\]
उत्तर
We have:
`3 cot θ=4`
`cotθ= 4/3`
Since we know that in right angle triangle
`cot θ=" Base"/"Perpendicular"`
`cot θ=" Base"/ "Hypotenuse"`
`sinθ = "Prependicular"/ "Hypotenuse" `
`"Hypotenuse"= sqrt(("Perpendicular")^2+("Base")^2)`
`"Hypotenuse"=sqrt((3)^2+(4)^2)`
`"Hypotenuse"=sqrt25`
`"Hypotenuse"=5`
Now, we find `(4 cosθ- sin θ)/(2 cos θ+sin θ)`
⇒ `(4 cosθ- sin θ)/(2 cos θ+sin θ)=(4xx 4/5-3/5)/(2xx4/5+3/5)`
⇒`(4 cosθ- sin θ)/(2 cos θ+sin θ) (16/5-3/5)/(8/5+3/5)`
⇒`(4 cosθ- sin θ)/(2 cos θ+sin θ)=``(13/5)/(11/5)`
⇒`(4 cosθ- sin θ)/(2 cos θ+sin θ) = 13/11`
Hence the value of `(4 cosθ- sinθ)/(2 cos θ+sin θ) "is" 13/11`
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