Question

if 4tanθ=3 evaluate 4sinθ-cosθ+1/4sinθ+cosθ-1

Answer 1

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! ☺☻☺

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! ☺☻☺