Question

If 5 tan θ − 4 = 0, then the value of \[\frac{5 \sin \theta - 4 \cos \theta}{5 \sin \theta + 4 \cos \theta}\] is:

पर्याय

• \[\frac{5}{3}\]

• \[\frac{5}{6}\]

•  0

• \[\frac{1}{6}\]

Answer 1

0

Explanation:

Given that: `5 tan θ-4=0`.We have to find the value of the following expression

`(5 sin θ-4 cos θ)/(5 sin θ+4 cos θ)`

Since `5 tan θ-=0 ⇒ tan θ=4/5` 

We know that:`tan θ= "Prependicular"/"Base"` 

`⇒"Base"=5`

`⇒"Perpendicular"=4`

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

`⇒"Hypotenuse"=sqrt(16+25)`

⇒ `"Hypotenuse"=sqrt41`

Since `sinθ ="Perpendicular"/"Hypotenuse" and Cos θ ="Base"/"Hypotenuse"`

Now we find

`( sin θ-4 cos θ)/(5 sinθ+4 cos θ)`

= `(5xx4/sqrt41-4xx5/sqrt41)/(5xx4/sqrt41+4xx5/sqrt41)`

=`(20/sqrt41-20/sqrt41)/(20/sqrt41+20/sqrt41)` 

= 0