First, cos (a + b) = 4 / 5. Cos (a-b) = - 4 / 5. A + B ∈ [7pi / 4,2pi]. A-B ∈ [3pi / 4, PI]. Cos2a =? Second, prove tan（ The second problem proves that Tan (θ + π / 4) = [Tan θ + 1] / [1 - Tan θ]

First, cos (a + b) = 4 / 5. Cos (a-b) = - 4 / 5. A + B ∈ [7pi / 4,2pi]. A-B ∈ [3pi / 4, PI]. Cos2a =? Second, prove tan（ The second problem proves that Tan (θ + π / 4) = [Tan θ + 1] / [1 - Tan θ]

Because: cos (a + b) = 4 / 5, a + B ∈ [7pi / 4, 2pi]. So: sin (a + b) = - 3 / 5
Because: cos (a-b) = - 4 / 5, A-B ∈ [3pi / 4, PI]. So: sin (a-b) = 3 / 5
So: cos2a = cos [(a + b) + (a-b)] = cos (a + b) cos (a-b) - sin (a + b) sin (a-b)
=4/5*(-4/5)-(-3/5)*(3/5)=-7/25

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