Question

if 5tan alpha=4 , show that (5 sin alpha - 3 cos alpha) /(5 sin alpha +2cos alpha) - 1/6

Answer 1

if 5 tan alpha = 4

then

tan alpha= 4/5

 

now

(5 sin alpha– 3cos alpha) / (5 sin alpha + 2cos alpha)

divide by cos alpha in both numerator and denominator

(5 tan alpha – 3) / (5 tan alpha + 2)

 put the value of tan alpha

(4 – 3) / (4 + 2)

 = 1/6

Hope this will help you
Mark as brainliest if you like.....

Answer 2

$\huge{\boxed{\mathbb{ANSWER}}}$

Given : 5 tan ∝ = 4 ,

To show that : (5 sin ∝ - 3 cos ∝) /(5 sin ∝ +2 cos ∝)  = 1/6

Now let's start the proving :-

We have,

5 tan ∝ = 4 ⇒ tan∝ = 4/5

Now, (5 sin∝ - 3 cos ∝) / (5 sin ∝ + 2 cos ∝)  

5sin∝-3cos∝/cos∝ ÷ 5sin∝ / cos∝ + 2cos∝/cos∝

( Dividing numerator and denominator by cos∝ )

⇒ 5sin∝/cos∝ - 3cos∝/cos∝ ÷ 5sin∝/cos∝ + 2cos∝/cos∝

⇒ 5tan∝-3 / 5tan∝+2

⇒ 5×4/5-3 ÷ 5×4/5+2 { ∵ tan∝ = 4/5 )

⇒ 4-3/4+2 = 1/6

$\implies \boxed{\mathsf{(5\:sin\:alpha\:-\:3\:cos\:alpha)/(5\:sin\:alpha\:+\:2\:cos\:alpha)\:=\: 1/6}}$

$\huge{\boxed{\sf{HENCE\:IT\:IS\:PROVED!}}}$