If sin ⁡ 2 β is the geometric mean between sin ⁡ α and cos ⁡ α , then cos ⁡ 4 β is equal to

Question

If sin ⁡ 2 β is the geometric mean between sin ⁡ α and cos ⁡ α , then cos ⁡ 4 β is equal to, 2 sin 2 ⁡ π 4 - α, 2 cos 2 ⁡ π 4 - α, 2 cos 2 ⁡ π 2 + α, 2 sin 2 ⁡ π 4 + α

MARKS App · Accepted Answer

sin 2 ⁡ 2 β = sin ⁡ α cos ⁡ α cos ⁡ 4 β = 1 - 2 sin 2 ⁡ 2 β = sin 2 ⁡ α + cos 2 ⁡ α - 2 sin ⁡ α cos ⁡ α = sin ⁡ α - cos ⁡ α 2 = 2 sin α · 1 2 - cos α 1 2 2 = 2 sin ⁡ α cos ⁡ π 4 - cos ⁡ α sin ⁡ π 4 2 = 2 sin ⁡ α - π 4 2 = 2 sin 2 ⁡ π 4 - α

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