1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
If fx = sin x...
Question
If
f
(
x
)
=
sin
x
+
cos
x
, then the number of solution of
f
(
x
)
=
[
f
(
π
10
)
]
, for
x
∈
(
0
,
4
π
)
is
(where [.] represent greatest integer function)
Open in App
Solution
We know that,
f
(
π
10
)
=
sin
π
10
+
cos
π
10
⇒
f
(
π
10
)
=
√
2
sin
(
π
10
+
π
4
)
Now,
sin
π
4
<
sin
(
π
10
+
π
4
)
<
sin
π
2
1
√
2
<
sin
(
π
10
+
π
4
)
<
1
1
<
√
2
sin
(
π
10
+
π
4
)
<
√
2
So,
Now the general solution will be,
sin
x
+
cos
x
=
1
⇒
sin
(
π
4
+
x
)
=
1
√
2
⇒
π
4
+
x
=
2
n
π
+
π
4
⇒
x
=
2
n
π
Or
⇒
π
4
+
x
=
2
n
π
+
3
π
4
⇒
x
=
2
n
π
+
π
2
Hence,
x
=
π
2
,
2
π
,
5
π
2
Suggest Corrections
0
Similar questions
Q.
If
f
(
x
)
=
sin
x
+
cos
x
, then the number of solution of
f
(
x
)
=
[
f
(
π
10
)
]
, for
x
∈
(
0
,
4
π
)
is
(where [.] represent greatest integer function)
Q.
If
f
(
x
)
=
2
[
x
]
+
cos
(
[
−
π
]
x
)
, where
[
.
]
represents greatest integer function, then
Q.
If
f
(
x
)
=
sin
x
+
cos
x
, then the number of solution of
f
(
x
)
=
[
f
(
π
10
)
]
, for
x
∈
(
0
,
4
π
)
is
(where [.] represent greatest integer function)
Q.
If,
f
(
x
)
=
c
o
s
[
π
2
]
x
+
c
o
s
[
−
π
2
]
x
,
where [x] stands for greatest integer function, then
Q.
If
f
(
x
)
=
sin
{
[
x
+
5
]
+
{
x
−
{
x
−
{
x
}
}
}
}
for
x
∈
(
0
,
π
4
)
is invertible, where
{
.
}
and
[
.
]
represent fractional part and greatest integer functions respectively, then
f
−
1
(
x
)
is
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Watch in App
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Solve
Textbooks
Question Papers
Install app