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Byju's Answer
Standard XII
Mathematics
Algebra of Derivatives
The real part...
Question
The real part of
e
e
i
θ
is:
A
e
c
o
s
θ
[
c
o
s
(
s
i
n
θ
)
]
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B
e
c
o
s
θ
[
c
o
s
(
c
o
s
θ
)
]
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C
e
s
i
n
θ
[
s
i
n
(
s
i
n
θ
)
]
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D
e
s
i
n
θ
[
c
o
s
(
s
i
n
θ
)
]
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Solution
The correct option is
A
e
c
o
s
θ
[
c
o
s
(
s
i
n
θ
)
]
e
e
i
θ
=
e
c
i
s
θ
=
e
cos
θ
+
i
s
i
n
θ
=
e
cos
θ
×
e
i
(
s
i
n
θ
)
=
e
cos
θ
×
(
cos
(
sin
θ
)
+
i
sin
(
sin
θ
)
)
Hence, the real part is
e
cos
θ
(
cos
(
s
i
n
θ
)
)
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0
Similar questions
Q.
Real Part of
e
e
i
θ
is
Q.
For real vales of
θ
, how many number of the following will be positive?
a.
cos
(
cos
θ
)
b.
cos
(
sin
θ
)
c.
sin
(
cos
θ
)
d.
sin
(
sin
θ
)
Q.
Solve
cos
(
sin
θ
)
=
sin
(
cos
θ
)
.
Q.
Prove that the two conics
l
1
r
=
1
−
e
cos
θ
and
l
2
r
=
1
−
e
cos
(
θ
−
a
)
will touch one another, if
l
2
1
(
1
−
e
2
2
)
+
l
2
2
(
1
−
e
2
1
)
+
2
l
1
l
2
e
1
e
2
cos
α
=
2
l
1
l
2
.
Q.
Find the derivative of
y
=
e
sin
θ
with respect to
θ
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