Arturo O. answered 11/02/19
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cos2θ + cos2θ tan2θ = cos2θ (1 + tan2θ) = cos2θ(1 + sin2θ / cos2θ)
= cos2θ [(cos2 + sin2θ) / cos2θ] = cos2θ (1 / cos2θ) = 1