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Standard XII
Maths
Question
If
f
(
x
)
=
sin
x
+
cos
x
, which of the following is correct ?
f
(
x
)
is even and not periodic
f
(
x
)
is even and periodic
f
(
x
)
is odd and not periodic
f
(
x
)
is odd and periodic
f
(
x
)
is neither even nor odd but periodic
A
f
(
x
)
is even and not periodic
B
f
(
x
)
is even and periodic
C
f
(
x
)
is odd and not periodic
D
f
(
x
)
is odd and periodic
E
f
(
x
)
is neither even nor odd but periodic
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Solution
Verified by Toppr
f
(
x
)
=
sin
(
x
)
+
cos
(
x
)
f
(
−
x
)
=
sin
(
−
x
)
+
cos
(
−
x
)
=
−
sin
(
x
)
+
cos
(
x
)
f
(
x
)
+
f
(
−
x
)
=
2
cos
(
x
)
Hence the function is periodic but is neither odd nor even.
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