2sin^4x+3/4sin^2(2x)+5cos^4x-cos3xcosx=2+2cos²x
等式左边=2sin^4x+3sin^2xcos^2x+5cos^4x-(cos2xcosx-sin2xsinx)cosx
=sin^2x(2sin^2x+3cos^2x)+5cos^4x-(2cos^2x-1-2sin^2x)cos^2x
=2sin^2x+sin^2xcos^2x+5cos^4x-cos^2x+4sin^2xcos^2x
=2sin^2x+5sin^2xcos^2x+5cos^4x-cos^2x
=2sin^2x+5cos^2x-cos^2x
=2+2cos^2x
所以,2sin^4x+3/4sin^2(2x)+5cos^4x-cos3xcosx=2+2cos²x
2.这个写法没见过,姑且先按照我的想法算吧
设a、β为锐角,且a=(sina,-cosa),b=(-cosβ,sinβ),a+b=(√6/6,√2/2)
则有：sina-cosβ=√6/6,sinβ-cosa=√2/2
(a+b)^2=6/36+2/4=2/3,a^2=1,b^2=1,2ab=-4/3,ab=-2/3
利用cos^2β+sin^2β=1化简
得到sin(a-60°)=√6/6,同样可以求出sin(β-30°)=√6/6
a-60=β-30,a=30+β,cos(a-β)=cos30°=√3/2
(sina-cosβ)*(sinβ-cosa)=√12/12=√3/6
sinasinβ-sinacosa-cosβsinβ+cosacosβ=√3/6
sin(a+β)-(sin2a+sin2β)/2=√3/6
因为sin2a+sin2β=2sin(a+β)cos(a-β)
sin(a+β）-√3sin(a+β)=√3/6
sin(a+β）=-√3/[6(√3-1)]=-(√3+3)/12
cos(a+β)=√[1-sin^2(a+β)]
3.y=0.5sin2x+√2sin(45°+x)
x=2kπ+π/4时,Ymax=(1+2√2)/2
4.sina+cosa=√2sin(π/4+a)=1/2,sin(π/4+a)=√2/4
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