cos(a+b) + cos(a-b)
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Step-by-step explanation:
Explanation:
We need
(
x
+
y
)
(
x
−
y
)
=
x
2
−
y
2
cos
(
a
+
b
)
=
cos
a
cos
b
−
sin
a
sin
b
cos
(
a
−
b
)
=
cos
a
cos
b
+
sin
a
sin
b
cos
2
a
+
sin
2
a
=
1
cos
2
b
+
sin
2
b
=
1
Therefore,
L
H
S
=
cos
(
a
+
b
)
cos
(
a
−
b
)
=
(
cos
a
cos
b
−
sin
a
sin
b
)
(
cos
a
cos
b
+
sin
a
sin
b
)
=
cos
2
a
cos
2
b
−
sin
2
a
sin
2
b
=
cos
2
b
(
1
−
sin
2
a
)
−
sin
2
a
(
1
−
cos
2
b
)
=
cos
2
b
−
cos
2
b
sin
2
a
−
sin
2
a
+
cos
2
b
sin
2
a
=
cos
2
b
−
sin
2
a
=
R
H
S
Q
E
D
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