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Byju's Answer
Standard XII
Mathematics
Properties Derived from Trigonometric Identities
The equation ...
Question
The equation
e
sin
x
−
e
−
sin
x
−
4
=
0
has :
A
Infinite number of real roots.
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B
No real roots
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C
Exactly one real root
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D
Exactly four real roots
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Solution
The correct option is
A
No real roots
e
s
i
n
x
−
e
−
s
i
n
x
−
4
=
0
Let
e
sin
x
=
t
So, we get the following equation
t
+
1
t
=
4
⇒
t
2
−
4
t
−
1
=
0
⇒
t
=
−
(
−
4
)
±
√
4
2
−
4
(
1
)
(
−
1
)
2
=
4
±
2
√
5
2
⇒
t
=
2
+
√
5
or
2
−
√
5
e
sin
x
=
2
+
√
5
and
2
−
√
5
is not possible.
Hence, no solution exists.
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0
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