Question

if tan A 4/3 find the value of 2 sin A -3 cos A /2 sin A +3 cos A
​

Answer 1

Solution:-

Given

$\rm \tan A = \dfrac{4}{3} = \dfrac{p}{b}$

$\rm \: p = 4,b = 3 \: and \: h = x$

Using phythogoeros theorem

$\rm \: {h}^{2} = {p}^{2} + {b}^{2}$

$\rm \: {x}^{2} = {4}^{2} + {3}^{2}$

$\rm \: x {}^{2} = 16 + 9$

$\rm \: x = 5 = h$

So

$\rm \: p = 4,b = 3 \: and \: h = 5$

Now

$\rm \sin A = \dfrac{p}{h} = \dfrac{4}{5}$

$\rm \: \cos A = \dfrac{b}{h} = \dfrac{3}{5}$

put the value on given equation

$\rm \dfrac{2 \sin A - 3 \cos A}{2 \sin A + 3 \cos A}$

$\rm \: \dfrac{2 \times \dfrac{4}{5} - 3 \times \dfrac{3}{5} }{2 \times \dfrac{4}{5} + 3 \times \dfrac{3}{5} }$

$\rm \: \dfrac{ \dfrac{8}{5} - \dfrac{9}{5} }{\dfrac{8}{5} + \dfrac{9}{5} }$

$\rm \: \dfrac{ - 1}{5} \times \dfrac{5}{17}$

Answer is

$\to \rm \: \dfrac{ - 1}{17}$

Answer 2

Answer:-1/7

See the picture I have added to this for complete Explaination