ребят, помогите доказать тождество)
cos^2(45-a)-cos^2(60+a)-cos 75 sin(75-2a)=sin2a
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ребят, помогите доказать тождество)
cos^2(45-a)-cos^2(60+a)-cos 75 sin(75-2a)=sin2a
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(cos(45-a))^2 - (cos(60+a))^2 - cos75*sin(75-2a) =
(cos(45-a) - cos(60+a))*(cos(45-a) + cos(60+a)) - cos75*sin(75-2a) =
2sin(105/2)sin(15/2 + a) * 2cos(105/2)cos(15/2 + a) - cos75*sin(75-2a) =
sin105 * sin(15+2a) - cos75sin(75-2a) = sin(180-75) * sin(90-(75-2a)) - cos75*sin(75-2a) =
sin(75) * cos(75-2a) - cos75*sin(75-2a) = sin(75 - (75-2a)) = sin2a