Question

If 5 tan ∅ = 4, find the value of 5sin∅ - 3cos∅/5sin∅ + 2cos∅

Answer 1

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Here's ur answer!

Given 5 tan∅ = 4 => tan∅ = 4/5

now,

$\frac{5sin \theta - 3cos \theta}{5sin \theta + 2cos \theta} \\ \\ = \frac{5 \frac{sin \theta}{cos \theta} - 3 \frac{cos \theta}{cos \theta}}{5 \frac{sin \theta}{cos \theta} + 2 \frac{cos \theta}{cos \theta} }$

(Dividing the numerator and denominator by cos∅)


$= \frac{5tan \theta \: - 3}{5tan \theta \: + 2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:( \therefore \: tan \theta \: = \frac{sin \theta}{cos \theta} )$

$= \frac{5. \frac{4}{5} - 3}{ 5 . \frac{4}{5} + 2 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (using(i))$

$= \frac{4 - 3}{4 + 2} = \frac{1}{6}$

Answer 2

Heya !!
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★Trigonometry ★
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→Given : 5 tan ∅ = 4 ................eq. ( 1 )

→ To find : 5 sin ∅ - 3 cos ∅ / 5 sin ∅ + 2 cos ∅....................... ( 2 )



☛ From the first eq. we have ,

◾tan ∅ = 4/5.................( 3 )



◼☛Next , we'll be dividing both the numerator and the denominator with cos ∅ in the eq. ( 2 ) to make it tan ∅

So, dividing by cos ∅ throughout in eq. ( 2 ) , We get :-


️☛5 tan ∅ - 3 / 5 tan ∅ + 2

→» Now , we can substitute the value of tan ∅ = 4 / 5 from eq. ( 3 )


◾We have ,

$= > \frac{5 \times \frac{4}{5} - 3 }{5 \times \frac{4}{5} + 2} \\ \\ = > \frac{4 - 3}{4 + 2} \\ \\ = > \frac{1}{6}$



★Hence the required answer is 1 / 6 ✔
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️☛Important points
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=> Tan ∅ = perpendicular ( p ) / base ( b )

=> Sin ∅ / Cos ∅ = Tan ∅

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