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Byju's Answer
Standard XII
Mathematics
Properties Derived from Trigonometric Identities
The number of...
Question
The number of solutions for the equation
2
sin
−
1
√
x
2
−
x
+
1
+
cos
−
1
√
x
2
−
x
=
3
π
2
is
A
1
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B
2
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C
3
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D
Infinite
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Solution
The correct option is
A
2
2
sin
−
1
√
x
2
−
x
+
1
+
cos
−
1
√
x
2
−
x
=
3
π
2
For existence of domain of
sin
−
1
√
x
2
−
x
+
1
−
1
≤
√
x
2
−
x
+
1
≤
1
0
≤
x
2
−
x
+
1
≤
1
⇒
x
2
−
x
≤
0
x
∈
[
0
,
1
]
For
cos
−
1
√
x
2
−
x
0
≤
x
2
−
x
≤
1
⇒
x
2
−
x
≥
0
x
(
x
−
1
)
≥
0
x
∈
[
−
∞
,
0
]
∪
[
1
,
∞
]
Only two points are common in their domains i.e.
0
and
1
which also satisfies the given equation.
So option
B
is correct
Suggest Corrections
0
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