Question

if 4tana=3 then evaluate 4sina-cosa+1/4sina+cosa-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

Question: If 4tanA=3 then evaluate (4sinA-cosA+1)/(4sinA+cosA-1)

Answer:

The required answer is 13/11.

Step-by-step explanation:

Given:-

4tanA = 3

To find:-

The value of (4sinA - cosA + 1)/(4sinA + cosA - 1).

According to the question,

It is given that 4tanA = 3

⇒ tanA = 3/4 ____ (1)

As we know,

From the figure,

tanA = PQ/QR ____ (2)

From (1) and (2), we get

PQ = 3 and QR = 4

By the Pythagoras theorem,

$PR^2=PQ^2+QR^2$

$PR^2=3^2+4^2$

$PR^2=9+16$

$PR^2=25$

PR = 25 units

Then,

sinA = PQ/PR

       = 3/5

cosA = QR/PR

        = 4/5

So, the value of (4sinA - cosA + 1)/(4sinA + cosA - 1) is,

= $\frac{4\times\frac{3}{5}-\frac{4}{5}+1}{4\times\frac{3}{5} +\frac{4}{5}-1}$

= $\frac{\frac{12}{5}-\frac{4}{5}+1}{\frac{12}{5} +\frac{4}{5}-1}$

= $\frac{\frac{12-4+5}{5}}{\frac{12+4-5}{5}}$

= $\frac{13/5}{11/5}$

= 13/11

Final answer: The required answer is 13/11.

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