化简sin^2a+sin^2b+2sinasinbcos(a+b)

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化简sin^2a+sin^2b+2sinasinbcos(a+b)

sin^2a+sin^2b+2sinasinbcos(a+b)
=sin^2a+sin^2b+2sinasinb(cosacosb-sinasinb)
=(sin^2a-sin^2asin^2b)+(sin^2b-sin^2asin^2b)+2sinasinbcosacosb
=sin^2acos^2b+sin^2bcos^2a+2sinasinbcosacosb
=(sinacosb+sinbcosa)^2
=[sin(a+b)]^2