Question

If 4 tan a=3,then the value of (4 sin a_cos a/4 sin a+cos a ) is equal to​

Answer 1

$\Huge{\underline{\underline{\mathfrak{Question \colon}}}}$

If 4tan x = 3,then find the value of :

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

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

Given,

$\large{ \sf{4 \: tan \: x = 3}} \\ \\ \large{ \hookrightarrow \: \boxed{ \sf{tan \: x = \frac{3}{4} }}}$

Now,

$\large{\sf{ \frac{4sin \: x - cos \: x}{4sinx \: + cos \: x} }}$

Dividing numerator and denominator by cos x,we get :

$\large{ \longrightarrow \: \sf{ \frac{4tan \: x - 1}{4tan \: x + 1} }} \\ \\ \large{ \longrightarrow \: \sf{ \frac{4( \frac{4}{3}) - 1 }{4( \frac{4}{3}) + 1 } }} \\ \\ \large{ \longrightarrow \: \sf{ \frac{ \frac{16}{3} - 1 }{ \frac{16}{3} + 1} }} \\ \\ \large{ \longrightarrow \: \sf{ \frac{13}{19} }}$

Answer 2

☆☆refer to the attachment please