Question

17-If 4 tan x=3, then 4sinx-
COSX/4sinx+COS X):
O 2/3
O 1/3
O 1/2
O
3/4​

Answer 1

Step-by-step explanation:

4tanx = 3

tanx = 3/4

p/b =3/4

h^2=p^2+b^2

h^2=(3)^2+(4)^2

h^2=9+16

h^2=25

h=5

sinx=3/5

cosx=4/5

4sinx-cosx/4sinx+cosx

(4×3/5-4/5)/4×3/5+4/5

(12/5-4/5)/12/5+4/5

(8/5)/16/5

8/16

1/2 is the answer

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If 4 tan x = 3 then

$\displaystyle \sf{ \frac{4 \sin x - \cos x }{4 \sin x + \cos x } }$

• $\displaystyle \sf{ \frac{2}{3} }$

• $\displaystyle \sf{ \frac{1}{3} }$

• $\displaystyle \sf{ \frac{1}{2} }$

• $\displaystyle \sf{ \frac{3}{4} }$

EVALUATION

Here it is given that

4 tan x = 3

Now

$\displaystyle \sf{ \frac{4 \sin x - \cos x }{4 \sin x + \cos x } }$

Dividing both of the numerator and denominator by cos x we get

$\displaystyle \sf{ = \frac{4 \dfrac{\sin x}{ \cos x} - \dfrac{ \cos x}{ \cos x} }{4 \dfrac{\sin x}{ \cos x} + \dfrac{ \cos x}{ \cos x}} }$

$\displaystyle \sf{ = \frac{4 \tan x - 1}{4 \tan x + 1 } }$

$\displaystyle \sf{ = \frac{3 - 1}{3 + 1} }$

$\displaystyle \sf{ = \frac{2}{4} }$

$\displaystyle \sf{ = \frac{1}{2} }$

FINAL ANSWER

Hence the correct option is $\displaystyle \sf{ \frac{1}{2} }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If cosθ+secθ=√2,find the value of cos²θ+sec²θ

https://brainly.in/question/25478419

2. Value of 3 + cot 80 cot 20/cot80+cot20 is equal to

https://brainly.in/question/17024513

3. In a triangle, prove that (b+c-a)(cotB/2+cotC/2)=2a×cotA/2

https://brainly.in/question/19793971