Question

If 5 tanθ = 4
then
find the value of
$\bf \dfrac{5 \sin( \theta) - 3 \cos( \theta) }{5 \sin( \theta ) + 2 \cos( \theta) }$
​

Answer 1

Step-by-step explanation:

Given,

5tanθ = 4

tanθ = 4/5

tan θ = sinθ/cosθ

sinθ = 4

cosθ = 5

NOW ,

evaluate the given equation

5 sinθ - 3cosθ/5 sinθ + 2cos θ

= 5( 4 ) -3 ( 5 )/ 5( 4 )+ 2( 5 )

= 20- 15/20+10

= 5/30

= 1/6

hence the solution is 1/6

Answer 2

Solution:

Given,

→ 5 tan θ = 4

• We have to find the value of (5 sin θ - 3 cos θ)/(5 sin θ + 2 cos θ)

So,

→ 5 tan θ = 4

→ tan θ = 4/5

Now,

$\rm \dfrac{5 \sin \theta - 3 \cos \theta}{5 \sin \theta + 2 \cos \theta}$

Dividing both sides by cos θ, we get,

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

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

We know that,

$\sf \implies \dfrac{ \sin \theta}{ \cos \theta } = \tan \theta$

So,

$\rm \dfrac{5 \dfrac{ \sin \theta}{ \cos \theta } - 3}{ 5\dfrac{ \sin \theta}{ \cos \theta } + 2}$

$\rm = \dfrac{5 \tan \theta - 3}{ 5\tan \theta + 2}$

$\rm = \dfrac{5 \times \dfrac{4}{5} - 3}{ 5 \times \dfrac{4}{5} + 2}$

$\rm = \dfrac{4 - 3}{4+ 2}$

$\rm = \dfrac{1}{6}$

So,

$\rm \implies \dfrac{5 \sin \theta - 3 \cos \theta}{5 \sin \theta + 2 \cos \theta} = \dfrac{1}{6}$

•••♪