Question

if 3tanx=4 evaluate 3sinx+2cosx/3sinx-2cosx​

Answer 1

$\huge\purple {\mid {\fbox {\tt {Solution}}\mid}}$

sinx+cosx=37

Step-by-step explanation:

Given : If 3 tan x is equal to 4.

To find : The value of sin x + cos x ?

Solution :

3 tan x is equal to 4

i.e. 3\tan x=43tanx=4

\tan x=\frac{4}{3}tanx=34

The expression is sin x + cos x

Divide expression by cos x,

\sin x + \cos x=\frac{\sin x}{\cos x}+\frac{\cos x}{\cos x}sinx+cosx=cosxsinx+cosxcosx

\sin x + \cos x=\tan x+1sinx+cosx=tanx+1

\sin x + \cos x=\frac{4}{3}+1sinx+cosx=34+1

\sin x + \cos x=\frac{7}{3}sinx+cosx=37