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Byju's Answer
Standard XII
Mathematics
Theorems on Integration
Find the inte...
Question
Find the integrals of the function
cos
2
x
−
cos
2
α
cos
x
−
cos
α
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Solution
cos
2
x
−
cos
2
α
cos
x
−
cos
α
=
−
2
sin
2
x
+
2
α
2
sin
2
x
−
2
α
2
−
2
sin
x
+
α
2
sin
x
−
α
2
,
[
∵
cos
C
−
cos
D
=
−
2
sin
C
+
D
2
sin
C
−
D
2
]
=
sin
(
x
+
α
)
sin
(
x
−
α
)
sin
(
x
+
α
2
)
sin
(
x
−
α
2
)
=
[
2
sin
(
x
+
α
2
)
cos
(
x
+
α
2
)
]
[
2
sin
(
x
−
α
2
)
cos
(
x
−
α
2
)
]
sin
(
x
+
α
2
)
sin
(
x
−
α
2
)
=
4
cos
(
x
+
α
2
)
cos
(
x
−
α
2
)
=
2
[
cos
(
x
+
α
2
+
x
−
α
2
)
+
cos
(
x
−
α
2
−
x
−
α
2
)
]
=
2
[
cos
(
x
)
+
cos
α
]
=
2
cos
x
+
2
cos
α
∴
∫
cos
2
x
−
cos
2
α
cos
x
−
cos
α
d
x
=
∫
(
2
cos
x
+
2
cos
α
)
d
x
=
2
[
sin
x
+
x
cos
α
]
+
C
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