已知sin(a+b)*sin(a-b)=1/3,求:(1/4)(sin2a)^2+(sinb)^2+(cosa)^4=?
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已知sin(a+b)*sin(a-b)=1/3,求:(1/4)(sin2a)^2+(sinb)^2+(cosa)^4=?
已知sin(a+b)*sin(a-b)=1/3,求:(1/4)(sin2a)^2+(sinb)^2+(cosa)^4=?
已知sin(a+b)*sin(a-b)=1/3,求:(1/4)(sin2a)^2+(sinb)^2+(cosa)^4=?
1/4sin2a.sin2a+sinb.sinb+cosa.cosa.cosa.cosa
=sina^2*cosa^2+sinb^2+cosa^2*cosa^2
=cosa^2(sina^2+cosa^2)+sinb^2
=cosa^2+sinb^2
sin(a+b)sin(a-b)=1/3
(sinacosb+cosasinb)(sinacosb-cosasinb)=1/3
sina^2cosb^2-cosa^2sinb^2=1/3
(1-cosa^2)(1-sinb^2)-cosa^2sinb^2=1/3
[1+cosa^2sinb^2-(cosa^2+sinb^2)]-cosa^2sinb^2=1/3
1-(cosa^2+sinb^2)=1/3
cosa^2+sinb^2=2/3
所以1/4sin2a.sin2a+sinb.sinb+cosa.cosa.cosa.cosa=2/3
3 在三角形ABC中,已知(a2+b2)sin(A-B)=(a2-b2)sin(A+B) 求证:ABC是等腰或直角三角形(a^2+b^2)sin(A-B)=(a^2-b^2)sin(A+B),(sin^A+sin^B)sin(A-B)=(sin^A-sin^B)sin(A+B) sin^A*(sin(A+B)-sin(A-B))=sin^B*(sin(A-B)+sin(A+B)) sin^A*2c
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