Question

if 4 tan x = 3 then cos x + sin x / cos x - sin x is equal to. a) 1/7 b) -1/7 c) 7 d) -7​

Answer 1

Answer:

=7 option( c)

Step-by-step explanation:

4 tan x = 3

tan x=3/4

and cotx=4/3

Now( cos x + sin x )/  (cos x - sin x)

Dividing up and down by cosx

(cosx/cosx + sinx/cosx) /  (cos x/cosx - sin x/cosx)

=(1+tanx) / (1-tanx)

=(1+3/4)/(1-3/4)

=((4+3)/4) / (4-3)/4

=(7/4) / (1/4)

=7 option( c)

Answer 2

Given,

$\[4\tan x = 3\]$

$\[\frac{{\cos x + \sin x}}{{\cos x - \sin x}} = ?\]\left$

Solution,

Know that,

$\[ \Rightarrow \tan x = \frac{3}{4}\]$

Calculate the value,

$\[ = \frac{{\cos x + \sin x}}{{\cos x - \sin x}}\]$

Taking $\[{\cos x}\]$ as a common,

$\[ = \frac{{1 + \frac{{\sin x}}{{\cos x}}}}{{1 - \frac{{\sin x}}{{\cos x}}}}\]$

$\[ = \frac{{1 + \tan x}}{{1 - \tan x}}\]$

$\[ = \frac{{1 + \frac{3}{4}}}{{1 - \frac{3}{4}}}\]$

$\[ = \frac{7}{1}\]$

Hence the value is 7.

The correct option is (c), i.e. 7