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Byju's Answer
Standard XII
Mathematics
Domain and Range of Trigonometric Ratios
The number of...
Question
The number of paired solutions
(
x
,
y
)
of the equation
1
+
x
2
+
2
x
sin
(
cos
–
1
y
)
=
0
is
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Solution
sin
(
cos
−
1
y
)
=
−
(
x
+
1
x
)
2
;
x
≠
0
Only possibility is
sin
(
cos
−
1
y
)
=
±
1
& hence
x
=
±
1
if
x
=
1
⇒
sin
(
cos
−
1
y
)
=
−
1
⇒
Not possible
[
∵
0
≤
cos
−
1
y
≤
π
]
If
x
=
−
1
⇒
sin
(
cos
−
1
y
)
=
1
⇒
y
=
0
So
x
=
−
1
&
y
=
0
is the solution.
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Domain and Range of Trigonometric Ratios
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