Given Tan α + cot α = 52, α ∈ (π 4, π 2), find the values of COS 2 α and sin (2 α + π 4)

Given Tan α + cot α = 52, α ∈ (π 4, π 2), find the values of COS 2 α and sin (2 α + π 4)

∵ Tan α + cot α = 52, ∵ sin α cos α + cos α sin α = 52, then 2sin2 α = 52, sin2 α = 45, ∵ α ∈ (π 4, π 2), ∵ 2 α ∈ (π 2, π), ∵ Cos2 α = − 1 − sin22 α = 35, sin (2 α + π 4) = sin2 α. Cos π 4 + Cos2 α. Sin π 4 = 45 × 22 − 35 × 22 = 210

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