1-1/4sin^2 2A-sin^2B-cos^4Asin(A+B)=3/5sin(A-B)=-4/5
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1-1/4sin^2 2A-sin^2B-cos^4A
sin(A+B)=3/5
sin(A-B)=-4/5
1-1/4sin^2 2A-sin^2B-cos^4A
=1-sin^2Acos^2A-sin^2B-cos^4A
=1-cos^2A-sin^2B
sin(A+B)=sinAcosB+cosAsinB=3/5
sin(A-B)=sinAcosB-cosAsinB=-4/5
cosAsinB=7/10
sinAcosB=-1/10
sin^2Acos^2B=(1-cos^2A)(1-sin^2B)
=1-sin^2B-cos^2A+cos^2Asin^2B
=1-sin^2B-cos^2A+49/100
=1/100
1-sin^2B-cos^2A=-12/25
所以:1-1/4sin^2 2A-sin^2B-cos^4A=-12/25.
1-1/4sin^2 2A-sin^2B-cos^4A
=1-1/4+1/4(2cos^2A-1)^2-1+COS^2A-cos^4A
=cos^4A-cos^2A+COS^2A-cos^4A
=0
sin2A=2sinAcosA,所以sin^2 2A=4sin^2Acos^2A
所以
1-1/4sin^2 2A-sin^2B-cos^4A
=1-sin^2Acos^2A-sin^2B-cos^4A
=cos^2B-sin^2Acos^2A-cos^4A
=cos^2B-cos^2A(sin^2A+cos^2A)
=cos^2B-cos^2A
=(cosB-cosA)(cosB+cosA)
下面你再思考思考 我先吃饭
-12/25
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