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Byju's Answer
Standard XII
Mathematics
Domain and Range of Basic Inverse Trigonometric Functions
Q.34 If f(x) ...
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Q.34 If f(x) and g(x) are periodic functions with the same fundamental period where f(x) = sinαx + cosαx and g(x) = |sinx| + |cosx|, then α is equal to
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Similar questions
Q.
Let
f
(
x
)
=
cos
(
x
+
π
3
)
and
g
(
x
)
=
sin
(
x
−
π
6
)
be two functions. Which of the following is/are correct ?
( where
x
∈
[
0
,
2
π
]
)
Q.
Assertion :Fundamental period of
cos
x
+
cot
x
is
2
π
. Reason: If the period of
f
(
x
)
is
T
1
and the period of
g
(
x
)
is
T
2
, then the fundamental period of
f
(
x
)
+
g
(
x
)
is the L.C.M. of
T
1
and
T
2
.
Q.
If the function
f
(
x
)
=
λ
|
sin
x
|
+
λ
2
|
cos
x
|
+
g
(
λ
)
,
λ
∈
R
is periodic with fundamental period
π
2
,
then
Q.
sin
a
x
+
cos
a
x
and
|
cos
x
|
+
|
sin
x
|
are periodic functions of same fundamental period if
a
equals to
Q.
Assertion :
f
(
x
)
=
cos
x
and
g
(
x
)
=
∫
cos
x
d
x
are both periodic functions Reason: If a function is periodic, then its antiderivative is also a periodic function
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