Question

Tan x =3/2,then the value of 3sin x +2cos x / 3 sin x - 2 cos x= ?

Answer 1

Answer:-

Given:-

tan x = 3/2

We have to find:-

$\sf \dfrac{3 \sin x + 2 \cos x}{3 \sin \: x - 2 \cos \: x}$

Dividing both numerator and denominator by cos x we get,

$\implies \sf \: \dfrac{ \frac{3 \sin x + 2 \cos x}{ \cos x} }{ \frac{3 \sin x - 2 \cos x}{ \cos x} } \\ \\ \\ \implies \sf \: \dfrac{ \frac{3 \sin x}{ \cos x} + \frac{2 \cos x}{ \cos x} }{\frac{3 \sin x}{ \cos x} - \frac{2 \cos x}{ \cos x}}$

using sin A/cos A = tan A we get,

$\implies \sf \: \dfrac{3 \tan x + 2}{3 \tan x - 2}$

Substitute tan x = 3/2 .

$\implies \sf \: \dfrac{3 \big( \frac{3}{2} \big) + 2}{3 \big( \frac{3}{2} \big) - 2} \\ \\ \\ \implies \sf \: \dfrac{ \frac{9}{2} + 2}{ \frac{9}{2} - 2 } \\ \\ \\ \implies \sf \: \dfrac{ \frac{9 + 4} { \cancel{2}}}{ \frac{9 - 4}{ \cancel{2}} } \\ \\ \\ \implies \underline{ \underline{\sf \: \dfrac{13}{5} }}$

Answer 2

Step-by-step explanation:

given :

• Tan x =3/2,then the value of 3sin x +2cos x / 3 sin x - 2 cos x= ?

to find :

• 3sin x +2cos x / 3 sin x - 2 cos x= ?

solution :

• 3tanx+2/ 3 tan x -2

• x= 3/2

• 3(3/2) + 2 / 3 (3/2) -2

• 9/2 +2 / 9/2-2

• 9+4/2 / 9-4/2

• = 13/5