Question

If
$4 \tan(\theta \:) = 3$
then evaluate
$\frac{4 \sin\theta \: - \cos\theta \: + 1 }{4 \sin\theta \: + \cos\theta \: - 1 }$
please dont answer if you dont know it.​

Answer 1

Given :-

4tan∅ = 3

tan∅ = 3/4

Method 1 :-

You can solve further by taking ∅ = 37°.

sin 37° = 3/5

cos 37° = 4/5

( 4*(3/5) - (4/5) + 1 )

———————————

( 4*(4/5) + (4/5) - 1 )

( (8/5) + 1 )

——————

( 4 - 1 )

( 13/5)

———

3

13/15

Method 2 :-

Calculate sin∅ and cos∅ by forming a right angled triangle with perpendicular 3 and base as 4.

sin∅ = 3/5

cos∅ = 4/5

Putting values in Original Question :-

( 4sin∅ - cos∅ + 1 )

———————————

( 4sin∅ + cos∅ - 1 )

( 4*(3/5) - (4/5) + 1 )

———————————

( 4*(4/5) + (4/5) - 1 )

( (8/5) + 1 )

——————

( 4 - 1 )

( 13/5)

———

3

13/15

Method 3 :-

Simplify it in tan∅ and sec∅ and then use

1 + tan²∅ = sec²∅

Answer

So, answer of this question is 13/15

Thank you.

Have a Nice Day!