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Byju's Answer
Standard XII
Mathematics
Conditional Identities
If π 2< x <π,...
Question
If
π
2
<
x
<
π
,
the write the value of
2
+
2
+
2
cos
2
x
in the simplest form.
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Solution
We have,
2
+
2
+
2
cos
2
x
=
2
+
2
1
+
cos
2
x
=
2
+
2
.
2
cos
2
x
=
2
+
2
cos
x
=
2
-
2
cos
x
∵
π
2
<
x
<
π
=
2
1
-
cos
x
=
2
.
2
sin
2
x
2
=
2
sin
x
2
=
2
sin
x
2
∵
π
4
<
x
2
<
π
2
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Similar questions
Q.
If
f
x
=
1
-
sin
x
π
-
2
x
,
x
≠
π
2
k
,
x
=
π
2
is continuous at
x
=
π
2
,
then k = _______________.
Q.
f
(
x
)
=
k
cos
x
π
−
2
x
if
x
≠
π
2
3
if
x
=
π
2
is continuous at
x
=
π
2
Find
k
.
Q.
Let
f
(
x
)
=
⎧
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎨
⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪
⎩
1
−
sin
3
x
3
cos
2
x
,
i
f
x
<
π
2
a
,
i
f
x
=
π
2
b
(
1
−
sin
x
)
(
π
−
2
x
)
2
,
i
f
x
>
π
2
. If
f
(
x
)
is continuous at
x
=
π
2
, find
a
and
b
.
Q.
If
f
(
x
)
=
s
i
n
(
c
o
s
x
)
−
c
o
s
x
(
π
−
2
x
)
3
,
i
f
x
≠
π
2
=
k
,
i
f
x
=
π
2
is
continuous at
x
=
π
2
,
then k
=
Q.
If
tan
(
π
/
4
+
x
)
+
tan
(
π
/
4
−
x
)
=
a
, then
tan
2
(
π
/
4
+
x
)
+
tan
2
(
π
/
4
−
x
)
=
?
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