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Byju's Answer
Standard XII
Mathematics
General Solution of Trigonometric Equation
The equation ...
Question
The equation
81
sin
2
x
+
81
cos
2
x
=
30
has two roots in the
A
I quadrant
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B
II quadrant
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C
III quadrant
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D
IV quadrant
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Solution
The correct options are
A
I quadrant
B
II quadrant
C
III quadrant
D
IV quadrant
Let
81
sin
2
x
=
y
.
Then
81
cos
2
x
=
81
1
−
sin
2
x
=
81.
y
−
1
,
so that the given equation is equivalent to
y
+
81
y
−
1
=
30
y
2
−
30
y
+
81
=
0
solve the equation in
y
⇒
y
=
3
or
y
=
27
⇒
81
sin
2
x
=
3
or
81
sin
2
x
=
27
⇒
3
4
sin
2
x
=
3
or
3
4
sin
2
x
=
3
3
⇒
sin
2
x
=
1
4
or
sin
2
x
=
3
4
sin
x
=
±
1
2
or
sin
x
=
±
√
3
2
which gives two solutions of the given equation in each quadrant.
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0
Similar questions
Q.
The number of roots of the equation,
(
81
)
sin
2
x
+
(
81
)
cos
2
x
=
30
in the interval
[
0
,
π
]
is equal to:
Q.
Solve the following equation:
81
sin
2
x
+
81
cos
2
x
=
30
Q.
If
x
∈
[
0
,
2
π
]
, then the number of solutions of the equation
81
cos
2
x
+
81
sin
2
x
=
30
is
Q.
If the angles of a triangle
A
B
C
satisfy the equation
81
s
i
n
2
x
+
81
c
o
s
2
x
=
30
, then the triangle can be
Q.
If
x
ϵ
[
0
,
π
]
and
81
s
i
n
2
x
+
81
c
o
s
2
x
=
30
, then find number of values of
x
satisfy the given equation.
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Standard XII Mathematics
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