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Standard XI
Mathematics
NCERT
Question
Prove the following:
s
i
n
(
n
+
1
)
x
s
i
n
(
n
+
2
)
x
+
c
o
s
(
n
+
1
)
x
c
o
s
(
n
+
2
)
x
=
c
o
s
x
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Solution
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Use
c
o
s
A
c
o
s
B
+
s
i
n
A
s
i
n
B
=
c
o
s
(
A
−
B
)
L
H
S
=
s
i
n
(
n
+
1
)
x
s
i
n
(
n
+
2
)
x
+
c
o
s
(
n
+
1
)
x
c
o
s
(
n
+
2
)
x
=
cos
[
(
n
+
2
)
x
−
(
n
+
1
)
x
]
=
cos
x
=
R
H
S
Hence proved.
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