May i know how to solve this qn: 3sinxcos40degrees = 2+ cosxsin40degrees?

Solving for x in 3sinx cos40° = 2 + cosx
sin40°

Then we divide both sides by
3cos40°

sinx  = (2/3cos40°) + cosx
sin40°/(3cos40°)

Rearranging terms and simplifying we
get

sinx  - cosx(1/3)tan40° - (2/3cos40°)  =
0

if we let A = (1/3)tan40° and B = (2/3cos40°), the
equation is reduced to

sinx  - Acosx - B  =
0

Here we can't find any trigonometric identity that
transform the equation into a single trigonometric
function.

So we will apply the GUESS & SEE method,
the objective is to find the value x to make sinx  - Acosx - B  equal to 0. It's quite
discouraging to imagine the amount of work we need here but by carefully observing how
the value of sinx  - Acosx - B changes as we try several values of x will lessen our
work. Of course we need electronic calculator to accomplish
these.

Let's begin guessing

if
x=0°             sinx  - Acosx - B = -1.14997

if x=90°  
        sinx  - Acosx - B = 0.129728

Now it's clear that x
is between 0° and 90°, more likely nearer to 90° than
to 0°.

try x =70°       sinx  - Acosx - B
= -0.026242

try x = 75°      sinx  - Acosx - B
= 0.023262

Now it's obvious the x is almost halfway between
70° & 75°

try x = 72.5°   sinx  - Acosx - B
= -0.000662

Therefore x = 72.5° may already
be acceptable

I did use MS Excel What-If
Analysis-GoalSeek function and quickly generate result for x = 72.5668962°
with sinx  - Acosx - B = 0 rounded to 9th place