if 2sintheta minus1=0,show that 4coscubetheta minus 3cos theta=0
Answers
Step-by-step explanation:
We can firstly factorise our original equation to make it become:
sin
θ
(
1
+
2
cos
θ
)
=
0
Therefore, if we set the two parts to zero separately that will make the equation work. For example, if
sin
θ
=
0
, then
0
⋅
(whatever the other part becomes) will indeed
=
0
.
So, separately we will make the two parts
=
0
. Starting with the left part, if
sin
θ
=
0
,
θ
=
0
o
,
180
o
,
360
o
... For the remainder of this question I will consider only the domain
0
o
≤
θ
≤
360
o
.
Then, we make the other part
=
0
. This means that
1
+
2
cos
θ
=
0
, by rearranging this becomes
cos
θ
=
−
1
2
. By solving with a calculator, our principal value is
120
o
.
240
o
is also a solution since if we consider how
cos
θ
reflects then we can obtain the above solution by doing
360
−
120
.
Our final solutions for
θ
are
0
o
,
120
o
,
180
o
,
240
o
and
360
o
, within the restricted domain
0
o
≤
θ
≤
360
o
. You can test all of these by substituting them into the original equation and they will indeed produce zero.
Answer:
here theta =30 degrees
sub 30 degree we get required solution...
