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Byju's Answer
Standard XII
Mathematics
Domain and Range of Basic Inverse Trigonometric Functions
If cos-1x+c...
Question
If
cos
−
1
x
+
cos
−
1
y
+
cos
−
1
z
=
3
π
, then value of
∑
x
y
equals
A
-3
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B
0
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C
3
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D
-1
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Solution
The correct option is
C
3
As
0
≤
c
o
s
−
1
θ
≤
π
For
c
o
s
−
1
x
+
c
o
s
−
1
y
+
c
o
s
−
1
z
=
3
π
this to true
⇒
c
o
s
−
1
x
=
c
o
s
−
1
y
=
c
o
s
−
1
z
=
π
⇒
x
=
y
=
z
=
−
1
∴
∑
x
y
=
x
y
+
y
z
+
z
x
=
(
−
1
)
2
+
(
−
1
)
2
+
(
−
1
)
2
=
3
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Similar questions
Q.
If
cos
−
1
x
+
cos
−
1
y
+
cos
−
1
z
=
3
π
,
then the value of
x
y
+
y
z
+
z
x
=