show that cos^2a =1+cos^2a/2
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Well we know that for two angles
A
,
B
it holds that
cos
(
A
+
B
)
=
cos
A
cos
B
−
sin
A
⋅
sin
B
hence for
A
=
B
you get
cos
(
2
A
)
=
cos
2
A
−
sin
2
A
But
sin
2
A
=
1
−
cos
2
A
hence
cos
(
2
A
)
=
cos
2
A
−
(
1
−
cos
2
A
)
=
2
cos
2
A
−
1
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