证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2B=1

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证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2B=1

证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2B=1
证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2
证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2B=1

证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2证明 sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2B=1
Sin^2A+Sin^2B-Sin^2ASin^2B+Cos^2ACos^2B
=Sin^2A(1-Sin^2B) + Sin^2B + Cos^2ACos^2B
=Sin^2ACos^2B+ Cos^2ACos^2B + Sin^2B
=Cos^2B+ Sin^2B
=1

=sin^2A(1-sin^2B)+sin^2B+cos^2Acos^2B
=sin^2Acos^2B+sin^2B+cos^2Acos^2B
=cos^2B+sin^2B
=1

证明:
sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2B
=sin²A*(1-sin²B)+sin²B+(1-sin²A)(1-sin²B)
=sin²A-sin²Asin²B+sin²B +1-sin²A-sin²B+sin²Asin²B
=1
∴ sin^2A+sin^2B-sin^2A*sin^2B+cos^2A*cos^2B=1