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Byju's Answer
Standard XII
Mathematics
General Solution of Trigonometric Equation
Find the set ...
Question
Find the set of value of
x
satisfying the equality
sin
(
x
−
π
4
)
−
cos
(
x
−
π
4
)
=
1
and the inequality
2
cos
7
x
cos
3
+
sin
3
>
2
cos
2
x
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Solution
sin
(
x
−
π
4
)
−
cos
(
x
−
π
4
)
=
1
sin
x
√
2
−
1
√
2
cos
x
−
[
cos
A
√
2
+
sin
A
√
2
]
=
1
√
2
sin
x
2
π
/
7
=
1
sin
x
=
1
√
2
⇒
x
=
45
o
2
cos
7
x
cos
3
+
sin
3
>
2
cos
2
x
→
π
T
(
L
C
M
of
2
π
7
,
π
)
⇒
2
π
sin
x
=
±
√
2
x
=
π
4
,
3
π
4
(
1
)
π
4
⇒
2
cos
7
π
/
4
√
2
(
cos
3
√
2
+
sin
3
√
2
)
>
2
cos
π
/
2
1
cos
(
3
−
π
/
4
)
>
1
1
cos
(
3
−
π
/
4
)
<
0
>
1
x
=
π
/
4
is not solution
(
2
)
3
π
4
⇒
2
cos
21
π
4
√
2
cos
(
3
−
π
/
4
)
>
2
cos
3
π
/
2
2
(
−
1
/
√
2
)
√
(
−
v
e
)
>
1
−
1
|
cos
(
3
−
π
/
4
)
|
>
1
x
=
3
π
4
x
=
2
n
π
+
3
π
/
4
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0
Similar questions
Q.
If
x
=
n
π
2
,
satisfies the equation
sin
x
2
−
cos
x
2
=
1
−
sin
x
& the inequality
∣
∣
∣
x
2
−
π
2
∣
∣
∣
≤
3
π
4
,
then
Q.
The value of
x
in
(
0
,
π
2
)
satisfying
√
3
−
1
sin
x
+
√
3
+
1
cos
x
=
4
√
2
is
Q.
Find the value of
sin
x
1
+
cos
x
at
x
=
π
4
Q.
The value of x in
(
0
,
π
/
2
)
satisfying the equation
√
3
−
1
sin
x
+
√
3
+
1
cos
x
=
4
√
2
.
Q.
If
0
<
x
<
π
4
and
cos
x
+
sin
x
=
5
4
,
find the numerical values of
cos
x
−
sin
x
.
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