化简[tan(π/4+α)cos2α]/[2cos^2(π/4-α)]

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化简[tan(π/4+α)cos2α]/[2cos^2(π/4-α)]

化简[tan(π/4+α)cos2α]/[2cos^2(π/4-α)]
化简[tan(π/4+α)cos2α]/[2cos^2(π/4-α)]

化简[tan(π/4+α)cos2α]/[2cos^2(π/4-α)]
[tan(π/4+α)cos2α]/[2cos^2(π/4-α)]
=[(tana+1)/(1-tan²a) × (cos²a-sin²a)]/(cosa+sina)²
=[1/(1-tana) × (cosa-sina)] /(cosa+sina)²
=[cosa/(cosa-sina) × (cosa-sina)]/(cosa+sina)²
=cosa×(cosa+sina)²
=cosa × (1+2sinacosa)
=cosa+2sinacos²a