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1) $sin^2( alpha - beta )+sin^2 beta +2sin( alpha - beta )sin beta cos alpha =sin^2 alpha$ $sin^2( alpha - beta )+sin^2 beta +sin( alpha - beta )(sin( beta - alpha )+sin( alpha + beta ))=sin^2 alpha$ $sin^2 beta +sin( alpha - beta )sin( alpha + beta )=sin^2 alpha$ $sin^2 beta + frac{cos2 beta -cos2 alpha }{2} =sin^2 alpha$ $2sin^2 beta +cos2 beta -cos2 alpha =2sin^2 alpha$ $2sin^2 beta +1-2sin^2 beta -1+2sin^2 alpha =2sin^2 alpha$
$2sin^2 alpha =2sin^2 alpha$ а значит $sin^2( alpha - beta )+sin^2 beta +2sin( alpha - beta )sin beta cos alpha =sin^2 alpha$ ч.т.д.