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Mathematics
Problem
37. Prove the power-reducing identities: (a) `
sin
2
u
=
1
−
cos
2
u
2
\sin ^{2} u=\frac{1-\cos 2 u}{2}
sin
2
u
=
2
1
−
c
o
s
2
u
` (b) `
cos
2
u
=
1
+
cos
2
u
2
\cos ^{2} u=\frac{1+\cos 2 u}{2}
cos
2
u
=
2
1
+
c
o
s
2
u
`
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