Question

If 4 tan Q = 3, evaluate

/ 4 sin Q – cos Q + 1 \
| ----------------------------- |
\ 4 sin Q + cos Q –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


or


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! ☺

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Answer 2

answer is 13/11

for solution refer to above pic