Question

if 4 tan= 3, evaluate (4 sin- cos+1÷4 sin+ cos-1)

Answer 1

4tan = 3 ⇒ tan = 3/4
we know, tan = perpendicular/base
so, after comparing , perpendicular = 3 and base = 4
∴ hypotenuse = √(3² + 4²) = 5
now, sin = perpendicular/hypotenuse = 3/5
cos = base/hypotenuse = 4/5

now, (4sin - cos + 1)/(4sin + cos - 1)
= (4 × 3/5 - 4/5 + 1)/(4 × 3/5 + 4/5 - 1)
= (12 - 4 + 5)/(12 + 4 - 5)
= 13/11

Answer 2

Hey there! ☺☻☺

Given,
4 tan = 3
∴ tan = 3/4

As we know,
Tan  = Perpendicular / base
Tan  = 3/4
Now,
Hypotenuse = √3² + 4² = √9+16 = √25 = 5

Using this, we can find:
Sin = Perpendicular / Hypotenuse = 3/5
Cos = Base / Hypotenuse = 4/5

ATQ,
(4sin - cos + 1)/(4sin + cos - 1) 
= (4 × 3/5 - 4/5 + 1)/(4 × 3/5 + 4/5 - 1)   [putting values]
= (12 - 4 + 5)/(12 + 4 - 5) 
= 13/11

Hope It Helps You! ☺☻☺