1. Sin32°sin42-cos3°cos42° 2.упростите А)√2cosα-2cos(45+α)/2sin(45°+α)-√2sinα Б)sin2α/cos²α-sin²α 3.дано sinα=9/41 ,

1. Sin 32° * sin 42 - cos 32° * cos 42° = sin ( 32 - 42 ) = sin ( - 10 ) = - sin 10 ; 2 . А ) ( √2 * cos α - 2 * cos ( 45 + α ) ) / ( 2 * sin ( 45° + α ) - √2 * sin α ) = ( √2 * cos α - 2 * ( √2 / 2 * cosa - √2 / 2 * sina ) / ( 2 * ( √2 / 2 * sina + √2 / 2 * cosa ) - √2 * sin α ) = ( √2 * cos α - √2 * cosa + √2 * sina ) / ( √2 * sina + √2 * cosa - √2 * sin α ) = √2 * sina / √2 * cosa = sina / cosa = tga ; Б ) sin2α / ( cos ² α - sin²α ) = sin2a / cos2a = tg2a ;3. sinα = 9 / 41, 90° < α < 180°. sin ( α + 45°) = √2 / 2 * sina + √2 / 2 * cosa ; cosa ^ 2 = 1 - sina ^ 2 = 1 - ( 9 / 41 ) ^ 2 = 1 - 81 / 1681 = ( 1681 - 81 ) / 81 = 1600 / 81 ; cosa = + - 40 / 9. Так как, 90° < α < 180°, тогда cosa = - 40 / 9 ; Значит, sin ( α + 45°) = √2 / 2 * sina + √2 / 2 * cosa = √2 / 2 * 9 / 41 - √2 / 2 * 40 / 9 = √2 / 2 * ( 9 / 41 - 40 / 9 ) = √2 / 2 * ( 81 - 1640 ) / 369 = √2 / 2 * 1559 / 369 = √2 * 1559 / 738.