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已知A,B,C是△ABC的三个内角,F(x)=Cos2x+5/2sinAsin...

∵A+π属于(π/2,3π2) 又sin(A+π/4)=7根号2/10 ∴cos(A+π/4)=-根号2/10 sinA=sin[(A+π/4)-π/4]=4/5 f(x)=cos2x+5/2*4/5*sinx=1-2sin²x+2sinx=-2(sinx-1/2)²+3/2 当sinx=1/2时f(x)max=3/2 当sinx=-1时f(x)min=-3

∵ f(x) = 2x²+4xsinA+3cosA 有且只有一个零点 ∴ △ = (4sinA)²-4*2*3cosA=0 ∴ 2sin²A-3cosA=0 ∴ 2-2cos²A-3cosA=0 2cos²A+3cosA-2=0 (cosA+2)(2cosA-1)=0 2cosA-1=0 cosA=1/2 A=60° 第二问: S=3√3 1/2bcsinA=3√3 bc=6√...

f(x)=3sin^2(x)+5cos^2(x)+2sinxcosx-4 =3sin²x+3cos²x+2cos²x+2sinxcosx-4 =3+(1+cos2x)+sin2x)-4 =sin2x+cos2x =√2(√2/2sin2x+cos2x) =√2sin(2x+π/4) f(x)的周期T=2π/2=π 由2kπ-π/2≤2x+π/4≤2kπ+π/2,k∈Z 得kπ-3π/8≤x≤kπ+π/8,k∈Z...

f(X)=√3/2sin2x-1/2cos2x-1=sin(2x-π/6)-1 g(x)=f(x+π/6)=sin(2x+π/6)-1 ①f(C)=sin(2C-π/6)-1=0 2C-π/6=π/2 C=π/3 sinB=3sinA=sin(A+C) 5/2sinA=√3/2cosA sinA=√21/14 sinB=3√21/14 有正弦定理得 a=3/4 b=9/4 ②g(B)=0 B=π/6 m*n=cosA+√3/2(sin...

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