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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Allied Angles
The value of ...
Question
The value of cos (36° − A) cos (36° + A) + cos (54° + A) cos (54° − A) is
(a) sin 2A
(b) cos 2A
(c) cos 3A
(d) sin 3A
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Solution
(b) cos 2A
cos
(
36
°
-
A
)
cos
(
36
°
+
A
)
+
cos
(
54
°
+
A
)
cos
(
54
°
-
A
)
=
cos
(
36
°
-
A
)
cos
(
36
°
+
A
)
+
sin
90
°
-
(
54
°
+
A
)
sin
90
°
-
(
54
°
-
A
)
Since
sin
(
90
°
-
θ
)
=
cos
θ
=
cos
(
36
°
-
A
)
cos
(
36
°
+
A
)
+
sin
(
36
°
-
A
)
sin
(
36
°
+
A
)
=
cos
(
36
°
+
A
-
36
°
+
A
)
Using
cos
(
A
-
B
)
formula
=
cos
2
A
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