Solution
Let α =
3π⁄
8
cos 2α = 2 cos2 α - 1 (Double angle formula)
cos 2(
3π⁄
8
)
=
2 cos2 (
3π⁄
8
)
- 1
cos (
3π⁄
4
)
=
2 cos2 (
3π⁄
8
)
- 1
1 + cos (
3π⁄
4
)
=
2 cos2 (
3π⁄
8
)
2 cos2 (
3π⁄
8
)
=
1 + cos (
3π⁄
4
)
2 cos2 (
3π⁄
8
)
=
1 +
-1⁄
√
2
=
√
2
- 1⁄
√
2
=
2 -
√
2
⁄
2
cos2 (
3π⁄
8 )
=
2 -
√
2
⁄
4
∴ cos
3π⁄
8 = ±
√
2 -
√
2
⁄2
Solution
Let α =
3π⁄
8
cos 2α = 1 - 2 sin2 α (Double angle formula)
cos 2(
3π⁄
8
)
=
1 - 2 sin2 (
3π⁄
8
)
cos (
3π⁄
4
)
=
1 - 2 sin2 (
3π⁄
8
)
2 sin2 (
3π⁄
8
) +
cos (
3π⁄
4
)
=
1
2 sin2 (
3π⁄
8
)
=
1 - cos (
3π⁄
4
)
2 sin2 (
3π⁄
8
)
=
1 - (-1⁄
√
2
)
=
√
2
+ 1⁄
√
2
=
2 +
√
2
⁄
2
sin2 (
3π⁄
8 )
=
2 +
√
2
⁄
4
∴ sin
3π⁄
8 = ±
√
2 +
√
2
⁄2