sin^2(α)+cosαcos（π/3+α）-sin^2(π/6-α)为定值,要证明

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sin^2(α)+cosαcos（π/3+α）-sin^2(π/6-α)为定值,要证明
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sin^2(α)+cosαcos（π/3+α）-sin^2(π/6-α)为定值,要证明
sin^2(α)+cosαcos（π/3+α）-sin^2(π/6-α)为定值,要证明

sin^2(α)+cosαcos（π/3+α）-sin^2(π/6-α)为定值,要证明
sin^2(a)+cosa*cos(pi/3+a)-sin^2(pi/6-a)
=sin^2(a)+cosa*(cospi/3cosa-sinpi/3sina)
-[sinpi/6cosa-sinacospi/6]^2
=sin^2(a)+cosa(1/2cosa-根号3/2sina)
-[1/2cosa-根号3/2sina]^2
=sin^2(a)+[1/2cos^2(a)-根号3/2sinacosa]
-[1/4cos^2(a)-根号3/2sinacosa+3/4sin^2(a)]
=[sin^2(a)-3/4sin^2(a)]+[1/2cos^2(a)-1/4cos^2(a)]-[根号3/2sinacosa-根号3/2sinacosa]
=[1/4sin^2(a)]+[1/4cos^2(a)]
=1/4[sin^2(a)+cos^2(a)]
=1/4
即无论a为何值,sin^2(α)+cosαcos（π/3+α）-sin^2(π/6-α)恒为定值 1/4

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sin^2(α)+cosαcos（π/3+α）-sin^2(π/6-α)为定值

3sinα=2cosα,则 cosα-sinα/cosα+sinα/ cos3sinα=2cosα,则cosα-sinα/cosα+sinα/cosα+sinα/cosα-sinα (1+sinα+cosα)*[sin(α/2)-cos(α/2)]/√(2+2cosα)化简 （3/2*π 利用和差角公式化简 (2)sin(π/3+α)+sin(π/3-α)(2)sin(π/3+α)+sin(π/3-α)(3)cos(π/4+α)-cos(π/4-α)(4)cos(60°+α)+cos(60°-α)(5)sin(α-β)cosβ+cos(α-β)sinβ(6)cos(α+β)cosβ+sin(α+β)sinβ 化简:sin(2π-α)cos(π+α)cos(11π/2-α)/cos(π-α)sin(3π-α)sin(-π-α)sin(9π/2+α) 化简sin(α-2π)+sin(-a-3π)cos(α-3π)/cos(π-α)-cos(-π-α)cos(α-4π) 已知0＜α＜π/2,且3sinα=4cosα求(sin^2α+2sinαcosα)/(3cos^2α-1)求cos^2α+sinαcosα sin(α+β)-2cosαsinβ/2cosαcosβ-cos(α+β) 设角a=-35π/6,则2sin(π+α)cos(π-α)-cos(π+α)/ 1+sin^2α+sin(π-α)-cos^2(π+α)sina=sin(-35π/6)=sin(-6π+π/6)=1/2 cosα=根号3/22sin(π＋α)cos(π-α)-cos(π+α)/ [1+sin^2α+sin(π-α)-cos^2(π+α)]=2（-sinα)(-cosα）+cosα/[1+sin² 化简sin(-π/2-α)sin(πα)cos(-α-π)/cos(π-α)sin(3π α) 求值【sin(2π-α)sin(π+α)cos(-π-α)】/【sin(3π-α)-cos(π-α)】 sinα=-2cosα,求sin^2α-3sinαcosα+1 已知3sinα=cosα,则sinα-2sinαcosα+3cosα+1= 已知sinα+3cosα=2,求（sinα-cosα）/(sinα+cosα)的值 已知sinα+3cosα=2,求（sinα-cosα）/(sinα+cosα)的值 sinα-2cosα分之sinα+cosα 化简sin(π/2+α)cos(3π-α)tan(π+α)/cos(π/2-α)cos(-α-π) 化简{sin(π+α)^3cos(-α)cos(π+α)}/{tan(π+α)^3cos(-π-α)^2} 若cosα>sinα,(-π/2