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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios Using Right Angled Triangle
If sin 2 θ-3 ...
Question
If
sin
2
θ
-
3
sinθ
+
2
cos
2
θ
=
1
,
then
θ
=
_______
.
Open in App
Solution
sin
2
θ
-
3
sin
θ
+
2
cos
2
θ
=
1
⇒
sin
2
θ
-
3
sin
θ
+
2
=
1
-
sin
2
θ
⇒
2
sin
2
θ
-
3
sin
θ
+
1
=
0
⇒
2
sin
2
θ
-
2
sin
θ
-
sin
θ
+
1
=
0
⇒
2
sin
θ
sin
θ
-
1
-
1
sin
θ
-
1
=
0
⇒
sin
θ
-
1
2
sin
θ
-
1
=
0
⇒
sin
θ
-
1
=
0
or
2
sin
θ
-
1
=
0
⇒
sin
θ
=
1
or
sin
θ
=
1
2
⇒
θ
=
90
°
or
θ
=
30
°
Here,
θ
cannot take the value 90º. For
θ
=
90
°
, the LHS of the given equation is not defined.
Thus, the value of
θ
is
30
°
.
If
sin
2
θ
-
3
sinθ
+
2
cos
2
θ
=
1
,
then
θ
=
30
°
.
Suggest Corrections
12
Similar questions
Q.
Solve for
θ
:
2
c
o
s
2
θ
+
3
s
i
n
θ
=
0
Q.
If
√
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tan
θ
=
3
sin
θ
, find the value of
sin
2
θ
−
cos
2
θ
, where
θ
≠
θ
is
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m
, m is
Q.
The smallest positive value of
θ
which satisfies the equation
2
c
o
s
2
θ
+
√
3
s
i
n
θ
+
1
=
0
Q.
Let
S
=
{
θ
∈
[
−
2
π
,
2
π
]
:
2
cos
2
θ
+
3
sin
θ
=
0
}
. Then the sum of the elements of S is?
Q.
Solve
2
cos
2
θ
−
√
3
sin
θ
+
1
=
0
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