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化简2cos²α-1/2tan(π/4-α)cos²(π/4-α)
题目详情
化简2cos²α-1/2tan(π/4-α)cos²(π/4-α)
▼优质解答
答案和解析
分子=2cos²α-1=cos2α
分母=2tan(π/4-α)cos²(π/4-α)
=2sin(π/4-α)/cos(π/4-α) *cos²(π/4-α)
=2sin(π/4-α)cos(π/4-α)
=sin((π/2-2α)
=cos2α
所以,原式=1
分母=2tan(π/4-α)cos²(π/4-α)
=2sin(π/4-α)/cos(π/4-α) *cos²(π/4-α)
=2sin(π/4-α)cos(π/4-α)
=sin((π/2-2α)
=cos2α
所以,原式=1
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